BA6933 Statistics Week 2 Quiz (Chapter 4 & 5 and 6)

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

a. 2

b. 4

c. 16

d. 12

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c

Revised probabilities of events based on additional information are

a. marginal probabilities.

b. complementary probabilities.

c. joint probabilities.

d. posterior probabilities.

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d

If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =

a. 0.2914.

b. 1.9700.

c. 0.6700.

d. 0.2100.

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d

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

a. 1/52

b. 4/52

c. 2/52

d. 3/52

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c

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

a. 0.650.

b. 0.390.

c. 0.169.

d. 0.400.

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d

Ten individuals attend a group ski lesson. Two individuals are selected from the group lesson to receive private lessons for a 15-minute period. In how many ways can the two individuals be selected if order is not important?

a. 5

b. 10

c. 45

d. 20

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c

Ten individuals attend a group ski lesson. Two individuals are selected from the group lesson to receive private lessons for a 15-minute period. In how many ways can the two individuals be selected if order is not important?

a. 5

b. 10

c. 45

d. 20

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c

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?

a. 64

b. 32

c. 16

d. 4

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a

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =

a. 0.80.

b. 0.00.

c. 0.15.

d. 0.20.

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a

A string of lights contains three lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability .10 of failing during a two-year period. If the lights fail independently of each other, what is the probability that a string of lights will remain bright for two years?

a. .729

b. .531

c. .27

d. .001

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a

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

a. 1,000.

b. 729.

c. 30.

d. 100.

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a

If a negative relationship exists between two variables, x and y, which of the following statements is true?

a. As x decreases, y decreases.

b. As x increases, y increases.

c. As x decreases, y stays the same.

d. As x increases, y decreases.

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d

In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to

a. the total number of elements in the data set.

b. one.

c. 100.

d. None of these alternatives are correct.

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c

The percent frequency of a class is computed by

a. dividing the relative frequency by 100.

b. adding 100 to the relative frequency.

c. multiplying the relative frequency by 100.

d. multiplying the relative frequency by 10.

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c

Which of the following is a graphical summary of a set of data in which each data value is represented by a dot above the axis?

a. Crosstabulation

b. Histogram

c. Box plot

d. Dot plot

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d

Data that provide labels or names for categories of like items are known as

a. label data.

b. category data.

c. categorical data.

d. quantitative data.

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c

In quality control applications, bar charts are used to identify the most important causes of problems. When the bars are arranged in descending order of height from left to right with the most frequently occurring cause appearing first, the bar chart is called a

a. Simpson,s chart.

b. Pareto diagram.

c. Stacked bar chart.

d. Cause-and-effect diagram.

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b

A frequency distribution is a tabular summary of data showing the

a. percentage of items in several classes.

b. relative percentage of items in several classes.

c. number of items in several classes.

d. fraction of items in several classes.

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c

Consider the following graphical summary.

This is an example of a _____.

a. percent frequency distribution

b. relative frequency distribution

c. bar chart

d. pie chart

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d

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

Undergraduate Major
Graduate School	Business	Engineering	Others	Total
Yes	70	84	126	280
No	182	208	130	520
Total	252	292	256	800

Of those students who are planning on going to graduate school, what percentage are majoring in engineering?

a. 10.5

b. 30.0

c. 40.4

d. 28.8

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b

For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal

a. 1.

b. 10.

c. 0.

d. -1.

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a

The variance of the sample

a. cannot be zero.

b. can never be negative.

c. can be negative.

d. cannot be less than one.

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b

Statements about the proportion of data values that must be within a specified number of standard deviations of the mean can be made using

a. Chebyshev's theorem.

b. A five-number summary.

c. Percentiles.

d. The empirical rule.

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a

Which of the following symbols represents the variance of the population?

a. μ

b. σ2

c. x̄

d. σ

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b

The geometric mean of 2, 4, 8 is

a. 4.67.

b. 16.

c. 5.0.

d. 4.0.

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d

Suppose a sample of 45 measurements gave a data set with a range of –8 to –22. The standard deviation of the measurements

a. is negative since all the numbers are negative.

b. cannot be computed since all the numbers are negative.

c. can be either negative or positive.

d. must be at least zero.

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d

Using the following data set of monthly rainfall amounts recorded for 10 randomly selected months in a two-year period, what is the five-number summary?

                     Sample data (in inches): 2, 8, 5, 0, 1, 5, 7, 5, 2, .5

a. 2, 5, 5, 5, .5

b. .5, 2, 5, 7, 8

c. 0, 1, 5, 5, 8

d. 0, 1, 3.5, 5, 8

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d

The difference between the largest and the smallest data values is the

a. range.

b. interquartile range.

c. variance.

d. coefficient of variation.

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a

In computing the mean of a sample, the value of ∑xi is divided by

a. n + 1.

b. n - 2.

c. n.

d. n - 1.

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c

The 75th percentile is referred to as the

a. third quartile.

b. second quartile.

c. first quartile.

d. fourth quartile.

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a

The measure of variability easiest to compute, but seldom used as the only measure, is the

a. range.

b. standard deviation.

c. variance.

d. interquartile range.

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a

Initial estimates of the probabilities of events are known as

a. prior probabilities.

b. conditional probabilities.

c. subjective probabilities.

d. posterior probabilities.

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a

If P(A) = 0.75, P(A ∪ B) = 0.86, and P(A ∩ B) = 0.56, then P(B) =

a. 0.11.

b. 0.67.

c. 0.56.

d. 0.25.

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b

What is the probability of randomly drawing a red ball from a bag that contains two red balls, five blue balls, one white ball, and three purple balls?

a. 1/2

b. 2/9

c. 2/11

d. 1/11

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c

The prior probabilities for events A1 and A2 are P(A1) = .25 and P(A2) = .75. The conditional probabilities of event B given A1 and A2 are P(B | A1) = .45, and P(B | A2) = .30. Using Bayes' theorem, what is the posterior probability P(A2 | B)?

a. .225

b. .775

c. .338

d. .667

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d

Which of the following is not a proper sample space when all undergraduates at a university are considered?

a. S = {age under 21, age 21 or over}

b. S = {in-state, out-of-state}

c. S = {a business major, not a business major}

d. S = {freshmen, sophomores}

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d

The symbol ∩ shows the

a. union of events.

b. intersection of two events.

c. sum of the probabilities of events.

d. sample space.

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b

Revised probabilities of events based on additional information are

a. joint probabilities.

b. complementary probabilities.

c. posterior probabilities.

d. marginal probabilities.

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c

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

a. 8.

b. 16.

c. 4.

d. 2.

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b

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. independent events.

b. non-mutually exclusive.

c. mutually exclusive.

d. complements of each other.

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c

A method of assigning probabilities based on historical data is called the

a. historical method.

b. relative frequency method.

c. subjective method.

d. classical method.

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b

In a binomial experiment

a. the probability changes from trial to trial.

b. the probability could change depending on the number of outcomes.

c. the probability does not change from trial to trial.

d. the probability could change from trial to trial, depending on the situation under consideration.

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c

If a random variable can assume one of five outcomes and the distribution is uniform, what is the probability function for this random variable?

a. f(x) = 1/5x

b. f(x) = x5

c. f(x) = .20

d. f(x) = 5

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c

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The expected value of x equals

a. 30

b. 100

c. 25

d. 24

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d

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.

Production
Per Month	Probability
1	0.01
2	0.04
3	0.10
4	0.80
5	0.05

The expected monthly production level is

a. 1.00

b. 3.00

c. 3.84

d. 4.00

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c

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

a. The trials are dependent

b. Exactly two outcomes are possible on each trial

c. The experiment has a sequence of n identical trials

d. The probabilities of the outcomes do not change from one trial to another

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a

A measure of the average value of a random variable is called a(n)

a. standard deviation.

b. coefficient of variation.

c. expected value.

d. variance.

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c

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

	Number of Goals	Probability
	0	0.05
	1	0.15
	2	0.35
	3	0.30
	4	0.15

What is the probability that in a given game the Lions will score less than 3 goals?

a. .85

b. .80

c. .55

d. .45

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c

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample at least 7 are female?

a. 0.0168

b. 0.0896

c. 0.8936

d. 0.1064

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d

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a

a. Normal distribution.

b. Hypergeometric probability distribution.

c. Poisson distribution.

d. Binomial distribution.

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c

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

Number Of Goals	Probability
0	0.05
1	0.15
2	0.35
3	0.30
4	0.15

What is the probability that in a given game the Lions do not score more than 2 goals?

a. 0.20

b. 0.55

c. 1.0

d. 0.95

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b

What is the probability that x is less than 5, given the function below?

f(x) =(1/10) e-x/10   x ≥ 0

a. 0.6065

b. 0.0606

c. 0.9393

d. 0.3935

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d

A negative value of z indicates that

a. the number of standard deviations of an observation is to the left of the mean.

b. the data has a negative mean.

c. a mistake has been made in computations, since z cannot be negative.

d. the number of standard deviations of an observation is to the right of the mean.

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a

Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours?

a. .0651

b. .5105

c. .5756

d. .4244

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a

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

a. 88.51

b. 90.51

c. 100.00

d. 93.2

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a

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the minimum weight of the middle 95% of the players?

a. 249

b. 151

c. 190

d. 196

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b

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

a. 50%

b. 38.49%

c. 38.59%

d. 76.98%

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d

The center of a normal curve is

a. is the standard deviation.

b. is the mean of the distribution.

c. always equal to zero.

d. cannot be negative.

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b

A continuous random variable may assume

a. only integer values in an interval or collection of intervals.

b. only fractional values in an interval or collection of intervals.

c. all the positive integer values in an interval.

d. all values in an interval or collection of intervals.

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d

The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. The probability that her trip will take exactly 50 minutes is

a. zero

b. 0.06

c. 0.20

d. 0.02

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a

The uniform distribution defined over the interval from 25 to 40 has the probability density function

a. f(x) = 1/25 for 0 ≤ x ≤ 25 and f(x) = 1/40 for 26 ≤ x ≤ 40

b. f(x) = 5/8 for 25 ≤ x ≤ 40 and f(x) = 0 elsewhere

c. f(x) = 1/40 for all x

d. f(x) = 1/15 for 25≤ x ≤ 40 and f(x) = 0 elsewhere

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d

The intersection of two mutually exclusive events

a. can be any positive value.

b. can be any value between 0 to1.

c. must always be equal to 0.

d. must always be equal to 1.

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c

An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?

a. 4

b. 32

c. 8

d. 16

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d

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible are possible?

a. 10

b. 5!

c. 20

d. 7

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a

If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A | B) =

a. 0.380.

b. 0.550.

c. 0.209.

d. 0.000.

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a

A string of lights contains three lights. The lights are wired in series, so that if any light fails the whole string will go dark. Each light has probability .10 of failing during a two-year period. If the lights fail independently of each other, what is the probability that a string of lights will remain bright for two years?

a. .531

b. .729

c. .27

d. .001

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b

If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =

a. 1.02.

b. 0.39.

c. 0.11.

d. 0.77.

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d

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. complements of each other.

b. independent events.

c. mutually exclusive.

d. non-mutually exclusive.

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c

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A ⏐ B) =

a. 0.0325.

b. 0.65.

c. 0.8.

d. 0.05.

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d

Initial estimates of the probabilities of events are known as

a. subjective probabilities.

b. posterior probabilities.

c. prior probabilities.

d. conditional probabilities.

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c

A method of assigning probabilities based upon judgment is referred to as the

a. subjective method.

b. classical method.

c. probability method.

d. relative method.

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a

Experiments with repeated independent trials will be described by the binomial distribution if

a. the trials are continuous.

b. the time between trials is constant.

c. each trial has exactly two outcomes whose probabilities do not change.

d. each trial result influences the next.

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c

A continuous random variable may assume

a. finite number of values in a collection of intervals.

b. only the positive integer values in an interval.

c. an infinite sequence of values.

d. any numerical value in an interval or collection of intervals.

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d

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

a. 0.0554

b. 0.28

c. 0.0036

d. 0.06

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a

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information.

Cups of Coffee	Frequency
0	700
1	900
2	600
3	300
	2,500

The variance of the number of cups of coffee is

a. 1

b. .9798

c. 2.4

d. .96

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d

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

a. 0.0036

b. 0.2800

c. 0.0600

d. 0.0555

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d

The following represents the probability distribution for the daily demand of computers at a local store.

Demand	Probability
0	0.1
1	0.2
2	0.3
3	0.2
4	0.2

The expected daily demand is

a. 2.0

b. 1.0

c. 4.0

d. 2.2

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d

An air traffic controller has noted that it clears an average of seven planes per hour for landing. What is the probability that during the next two hours exactly 15 planes will be cleared for landing?

a. .0033

b. .0651

c. .0989

d. Not enough information is given to answer the question.

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c

The expected value of a random variable is

a. the square root of the variance.

b. the value of the random variable that occurs most frequently.

c. the value of the random variable that should be observed on the next repeat of the experiment.

d. None of these alternatives are correct.

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d

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is

a. .008

b. .096

c. .8

d. .104

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b

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is

a. 3.46

b. 2.83

c. 20

d. 12

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d

The probability distribution that can be described by just one parameter is the

a. uniform.

b. exponential.

c. normal.

d. binomial.

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b

In a standard normal distribution, the range of values of z is from

a. minus infinity to infinity.

b. 0 to 1.

c. -1 to 1.

d. -3.09 to 3.09.

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a

Joe's Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day's sales in excess of $2200?

a. More information is needed

b. Store 2

c. Store 1

d. Store 1 and store 2 are equally likely

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d

In a standard normal distribution, the probability that Z is greater than zero is

a. 0.5.

b. equal to 1.

c. at least 0.5.

d. 1.96.

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a

x is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

a. 0.4931

b. 0.000

c. 0.0069

d. 0.9931

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c

z is a standard normal random variable. The P(z ≥ 2.11) equals

a. 0.9821

b. 0.4821

c. 0.0174

d. 0.5

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c

What is the mean of x, given the function below?

f(x) =(1/10) e-x/10    x ≥ 0

a. 10

b. 0.10

c. 1,000

d. 100

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a

The function that defines the probability distribution of a continuous random variable is a

a. normal function.

b. probability density function.

c. either normal of uniform depending on the situation.

d. uniform function.

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b

For a uniform probability density function,

a. the height of the function cannot be larger than one.

b. the height of the function is different for various values of x.

c. the height of the function decreases as x increases.

d. the height of the function is the same for each value of x.

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d

The probability density function for a uniform distribution ranging between 2 and 6 is

a. any positive value.

b. 0.25.

c. 4.

d. undefined.

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b

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?

a. 16

b. 4

c. 32

d. 64

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d

The symbol ∪ shows the

a. sample space.

b. sum of the probabilities of events.

c. union of events.

d. intersection of two events.

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c

In a random sample of 200 students, 55% indicated they have full-time jobs, while the other 45% have part-time jobs. Fifty of the 90 male students surveyed have a full-time job, and 60 of the females surveyed have a full-time job. What is the probability that a randomly selected student is female given they have a part-time job?

a. .23

b. .45

c. .56

d. .41

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c

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =

a. 0.12.

b. 0.62.

c. 0.68.

d. 0.60.

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c

If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A | B) =

a. 0.40

b. 0.22

c. 0.00

d. 0.45

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a

From a group of six people, two individuals are to be selected at random. How many selections are possible?

a. 36

b. 8

c. 12

d. 15

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d

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called the

a. counting rule for multiple-step random experiments.

b. counting rule for permutations.

c. counting rule for independent events.

d. counting rule for combinations.

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b

A collection of sample points is

a. an event.

b. an intersection.

c. a union.

d. a permutation.

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Solution

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a

The sample space refers to

a. the set of all possible experimental outcomes.

b. the sample size minus one.

c. any particular experimental outcome.

d. an event.

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a

The intersection of two mutually exclusive events

a. can be any value between 0 to1.

b. must always be equal to 1.

c. can be any positive value.

d. must always be equal to 0.

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d

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

a. 2.

b. 16.

c. 4.

d. 20.

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c

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

a. Binomial distribution.

b. Poisson distribution.

c. Normal distribution.

d. Uniform distribution.

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b

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The expected value of x equals

a. 25

b. 30

c. 100

d. 24

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d

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?

a. 0.0036

b. 0.28

c. 0.06

d. 0.0554

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d

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

	Number of Goals	Probability
	0	0.05
	1	0.15
	2	0.35
	3	0.30
	4	0.15

The expected number of goals per game is

a. 2.35

b. 2.5

c. 3

d. 2

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Solution

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a

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .0241

b. .9107

c. .1126

d. .0771

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Solution

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d

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information.

Cups of Coffee	Frequency
0	700
1	900
2	600
3	300
	2,500

The expected number of cups of coffee is

a. 1.5

b. 1

c. 1.7

d. 1.2

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d

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is

a. .096

b. .104

c. .8

d. .008

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a

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information.

Cups of Coffee	Frequency
0	700
1	900
2	600
3	300
	2,500

The variance of the number of cups of coffee is

a. .96

b. 2.4

c. 1

d. .9798

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Solution

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a

The Poisson probability distribution is used with

a. any random variable.

b. a continuous random variable.

c. a discrete random variable.

d. either a continuous or discrete random variable.

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c

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The standard deviation of assembly time (in minutes) is approximately

a. 1.3333

b. 1.1547

c. 0.5773

d. 0.1111

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b

The probability that a continuous random variable takes any specific value

a. depends on the probability density function.

b. is equal to zero.

c. is very close to 1.0.

d. is at least 0.5.

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b

z is a standard normal random variable. The P(1.05 ≤ z ≤ 2.13) equals

a. 0.4834

b. 0.3531

c. 0.8365

d. 0.1303

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d

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

a. 18.53%

b. 8.53%

c. 0.853%

d. 91.47%

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b

For a normal distribution, a positive value of z indicates that

a. the sample mean is smaller than the population mean.

b. all the observations must have had positive values.

c. the sample mean is larger than the population mean.

d. the area corresponding to the z is either positive or negative.

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c

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370?

a. – 1.53

b. .8264

c. 1.96

d. 1.50

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a

z is a standard normal random variable. The P(z ≥ 2.11) equals

a. 0.0174

b. 0.4821

c. 0.5

d. 0.9821

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a

The function that defines the probability distribution of a continuous random variable is a

a. normal function.

b. probability density function.

c. either normal of uniform depending on the situation.

d. uniform function.

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b

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .05

c. .025

d. .5

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d

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What percent of players weigh between 180 and 220 pounds?

a. 0.281%

b. 0.5762%

c. 57.62%

d. 28.81%

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c

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

a. 24.

b. 14.

c. 9.

d. 36.

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a

Revised probabilities of events based on additional information are

a. posterior probabilities.

b. complementary probabilities.

c. joint probabilities.

d. marginal probabilities.

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a

Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?

a. 25

b. 30

c. 32

d. 10

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c

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. complements of each other.

b. non-mutually exclusive.

c. independent events.

d. mutually exclusive.

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d

Females account for 65% of sales at a major retailer. Assume the probability of a customer being female is .65. The probability that a purchase made by a female exceeds $100 is .32, and the probability that a purchase made by a male exceeds $100 is .06. Suppose the manager is told that a customer made a purchase in excess of $100. What is the probability the customer was a female?

a. .65

b. .09

c. .91

d. .21

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c

Two events are mutually exclusive

a. if they have no sample points in common.

b. if their intersection is 0.5.

c. if their intersection is 1.

d. if most of their sample points are in common.

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a

A collection of sample points is

a. a permutation.

b. a union.

c. an event.

d. an intersection.

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c

The union of events A and B is the event containing all the sample points belonging to

a. A or B.

b. A or B or both.

c. B or A.

d. A or B, but not both.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.14.

b. 0.59.

c. 0.75.

d. 0.43.

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d

The prior probabilities for events A1 and A2 are P(A1) = .25 and P(A2) = .75. The conditional probabilities of event B given A1 and A2 are P(B | A1) = .45, and P(B | A2) = .30. Using Bayes' theorem, what is the posterior probability P(A2 | B)?

a. .225

b. .775

c. .338

d. .667

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d

The probability of an event is

a. the sum of the probabilities of the sample points in the event.

b. the minimum of the probabilities of the sample points in the event.

c. the maximum of the probabilities of the sample points in the event.

d. the product of the probabilities of the sample points in the event.

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a

If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∪ B) =

a. 0.65.

b. 0.55.

c. 0.75.

d. 0.10.

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b

In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is

a. all accounts from new customers and all accounts that are from 31 to 60 days past due.

b. all accounts fewer than 31 or more than 60 days past due.

c. all new customers whose accounts are between 31 and 60 days past due.

d. all new customers.

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a

If P(A ∩ B) = 0,

a. A and B are independent events.

b. P(A) + P(B) = 1.

c. either P(A) = 0 or P(B) = 0.

d. A and B are mutually exclusive events.

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d

If P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88, then P(B |A) =

a. 0.04.

b. 0.03.

c. 0.05.

d. 0.02.

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a

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

a. 0.650.

b. 0.390.

c. 0.400.

d. 0.169.

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c

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the

a. relative frequency method.

b. probability method.

c. classical method.

d. subjective method.

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c

Events A and B are mutually exclusive. Which of the following statements is also true?

a. P(A ∪ B) = P(A)P(B)

b. P(A ∪ B) = P(A) + P(B)

c. A and B are also independent.

d. P(A ∩ B) = P(A) + P(B)

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b

A description of the distribution of the values of a random variable and their associated probabilities is called a

a. bivariate distribution.

b. empirical discrete distribution.

c. probability distribution.

d. table of binomial probability.

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c

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

a. 0.0038

b. 0.02

c. 0.10

d. 0.0004

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a

The weight of an object, measured to the nearest gram, is an example of

a. a continuous random variable.

b. a nominal random variable.

c. a mixed type random variable.

d. a discrete random variable.

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d

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions' properties are satisfied by random variable x?

a. Hypergeometric

b. Poisson

c. Normal

d. Binomial

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b

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The variance of x equals

a. 84

b. 93.33

c. 85

d. 9.165

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a

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The expected value of x equals

a. 30

b. 100

c. 25

d. 24

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d

The amount of time a patient must wait to be seen at a doctor's office is an example of

a. a continuous random variable.

b. a discrete random variable.

c. either a continuous or a discrete random variable, depending on the type of doctor's office.

d. either a continuous or a discrete random variable, depending on the gender of the individual.

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a

The following represents the probability distribution for the daily demand of computers at a local store.

Demand	Probability
0	0.1
1	0.2
2	0.3
3	0.2
4	0.2

The expected daily demand is

a. 2.2

b. 1.0

c. 2.0

d. 4.0

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a

Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.

Number of
New Clients	Probability
0	0.05
1	0.10
2	0.15
3	0.35
4	0.20
5	0.10
6	0.05

The expected number of new clients per month is

a. 21

b. 0

c. 6

d. 3.05

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d

Random variable x has the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is

a. 2.333

b. 0.333

c. 0.500

d. 2.000

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a

Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.

a. continuous

b. discrete

c. intermittent

d. uniform

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a

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that there are no females in the sample is

a. 0.5000

b. 0.0778

c. 0.3456

d. 0.7780

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b

The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. The variance of the number of days Pete will catch fish is

a. .8

b. 2.4

c. .48

d. .16

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The appropriate probability distribution for the random variable is

a. binomial.

b. continuous.

c. either discrete or continuous depending on how the interval is defined.

d. discrete.

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d

Random variable x has the probability function f(x) = X/6, for x = 1, 2 or 3
The expected value of x is

a. 2.000.

b. 0.333.

c. 0.500.

d. 2.333.

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d

Which of the following is not a required condition for a discrete probability function?

a. Σf(x) = 0

b. Σf(x) = 1

c. f(x) ≥ 0 for all values of x

d. All of these choices are correct.

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a

The number of vehicle thefts in the parking lot of a shopping mall varies from month to month. Assume that the number of thefts (x) at the shopping mall has the following probability distribution.

The mean number of thefts per month is _____.

a. .70

b. 6

c. .175

d. 1.5

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a

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is

a. 20.

b. 144.

c. 12.

d. 3.46.

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c

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the

a. hypergeometric probability distribution.

b. exponential probability distribution.

c. binomial probability distribution.

d. Poisson probability distribution.

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a

The variance Var(x) for the binomial distribution is given by equation

a. n(1 - p).

b. np(1 - p).

c. np(1 - np).

d. np(n - 1).

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b

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

a. 0.4772

b. 0.9772

c. 0.0228

d. 0.5000

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b

A normal probability distribution

a. needs to have a mean of 0.

b. can have mean of any numerical value.

c. has a standard deviation of 0.

d. must have a standard deviation of 1 and a mean of 0.

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b

Given that z is a standard normal random variable, what is the probability that -2.51 ≤ z ≤ -1.53?

a. 0.0570

b. 0.4950

c. 0.9310

d. 0.4370

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a

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?

a. 0.4803

b. 3.06

c. -2.06

d. -1.97

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c

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

a. 0.50

b. 1.00

c. 0

d. any value between 0 to 1

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c

What is the probability that x is less than 5, given the function below?

f(x) =(1/10) e-x/10   x ≥ 0

a. 0.6065

b. 0.0606

c. 0.9393

d. 0.3935

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d

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What percentage of tires will have a life of 34,000 to 46,000 miles?

a. 88.49%

b. 38.49%

c. 50%

d. 76.98%

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d

A negative value of z indicates that

a. the number of standard deviations of an observation is to the left of the mean.

b. a mistake has been made in computations, since z cannot be negative.

c. the data has a negative mean.

d. the number of standard deviations of an observation is to the right of the mean.

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a

Which of the following is not a characteristic of the normal probability distribution?

a. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

b. The mean is equal to the median, which is also equal to the mode.

c. The total area under the curve is always equal to 1.

d. Symmetry

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a

What is the mean of x for the exponential distribution, , x ≥ 0?

a. .5

b. 0

c. 1.36

d. 2

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d

The probability density function for a uniform distribution ranging between 2 and 6 is

a. undefined.

b. 4.

c. 0.25.

d. any positive value.

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c

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .025

c. .5

d. .05

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c

Suppose a preliminary screening is given to prospective student athletes at a university to determine whether they would qualify for a scholarship. The scores are approximately normal with a mean of 85 and a standard deviation of 20. If the range of possible scores is 0 to 100, what percentage of students has a score less than 85?

a. 100%

b. 98.34%

c. 50%

d. 8.5%

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c

The probability distribution that can be described by just one parameter is the

a. exponential.

b. uniform.

c. normal.

d. binomial.

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a

For any continuous random variable, the probability that the random variable takes a value less than zero

a. is a value larger than zero.

b. is any number between zero and one.

c. is more than one, since it is continuous.

d. is zero.

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b

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.

a. 235

b. .03

c. 30

d. 75

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a

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.0559?

a. 0.4441

b. 1.50

c. -1.59

d. 0

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c

What is the mean of x for the exponential distribution, , x ≥ 0?

a. 2

b. .5

c. 0

d. 1.36

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a

What is the mean of x, given the function below?

f(x) =(1/10) e-x/10    x ≥ 0

a. 10

b. 100

c. 0.10

d. 1,000

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a

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

a. 76.98%

b. 38.59%

c. 38.49%

d. 50%

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a

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible are possible?

a. 7

b. 10

c. 5!

d. 20

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b

The intersection of two mutually exclusive events

a. can be any value between 0 to1.

b. must always be equal to 0.

c. can be any positive value.

d. must always be equal to 1.

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Solution

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b

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

a. 4

b. 16

c. 2

d. 12

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b

If P(A) = 0.75, P(A ∪ B) = 0.86, and P(A ∩ B) = 0.56, then P(B) =

a. 0.56.

b. 0.25.

c. 0.11.

d. 0.67.

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d

A graphical method of representing the sample points of an experiment is a

a. dot plot.

b. stacked bar chart.

c. tree diagram.

d. stem-and-leaf display.

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Solution

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c

Which of the following is not a proper sample space when all undergraduates at a university are considered?

a. S = {age under 21, age 21 or over}

b. S = {in-state, out-of-state}

c. S = {a business major, not a business major}

d. S = {freshmen, sophomores}

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d

In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B

a. cannot be determined with the information given.

b. cannot be larger than 0.4.

c. can be any value greater than 0.6.

d. can be any value between 0 to 1.

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b

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

a. 2/52

b. 4/52

c. 1/52

d. 3/52

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a

Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?

a. 25

b. 32

c. 30

d. 10

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b

If A and B are mutually exclusive, then

a. P(A) + P(B) = 0.

b. P(A ∩ B) = 1.

c. P(A) + P(B) = 1.

d. P(A ∩ B) = 0.

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d

If A and B are mutually exclusive, then

a. P(A) + P(B) = 0.

b. P(A ∩ B) = 1.

c. P(A) + P(B) = 1.

d. P(A ∩ B) = 0.

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d 

Posterior probabilities are computed using

a. the empirical rule.

b. relative frequency.

c. Bayes' theorem.

d. Chebyshev's theorem.

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c

Revised probabilities of events based on additional information are

a. posterior probabilities.

b. marginal probabilities.

c. joint probabilities.

d. complementary probabilities.

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a

A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial

a. head has a larger chance of appearing than tail.

b. tail has a better chance of appearing than head.

c. tail has same chance of appearing as the head.

d. tail can not appear.

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c

The prior probabilities for events A1 and A2 are P(A1) = .25 and P(A2) = .75. The conditional probabilities of event B given A1 and A2 are P(B | A1) = .45, and P(B | A2) = .30. Using Bayes' theorem, what is the posterior probability P(A2 | B)?

a. .667

b. .225

c. .338

d. .775

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a

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. non-mutually exclusive.

b. complements of each other.

c. independent events.

d. mutually exclusive.

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d

If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =

a. 1.02.

b. 0.11.

c. 0.39.

d. 0.77.

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d

The probability of at least one head in two flips of a coin is

a. 0.33.

b. 0.75.

c. 0.25.

d. 0.50.

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b

In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The complement of A is

a. all new customers.

b. all new customers whose accounts are between 31 and 60 days past due.

c. all accounts fewer than 31 or more than 60 days past due.

d. all accounts from new customers and all accounts that are from 31 to 60 days past due.

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c

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for independent events.

c. counting rule for combinations.

d. counting rule for permutations.

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c

If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =

a. 1.9700.

b. 0.6700.

c. 0.2914.

d. 0.2100.

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d

If a television fails with probability P(F) = .09, what is the probability that the television does not fail?

a. .09

b. .91

c. 1.09

d. Not enough information is given to answer the problem.

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b

If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪ B) =

a. 0.55.

b. 0.48.

c. 0.07.

d. 0.62.

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b

If A and B are mutually exclusive, then

a. P(A) + P(B) = 1.

b. P(A) + P(B) = 0.

c. P(A ∩ B) = 0.

d. P(A ∩ B) = 1.

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c

The probability of at least one head in two flips of a coin is

a. 0.25.

b. 0.50.

c. 0.33.

d. 0.75.

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d

Two events with nonzero probabilities

a. can be both mutually exclusive and independent.

b. are always mutually exclusive.

c. can not be both mutually exclusive and independent.

d. are always independent.

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c

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

a. larger than the probability of tails.

b. 0.

c. 1/2.

d. 1/16.

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c

The intersection of two mutually exclusive events

a. can be any positive value.

b. can be any value between 0 to1.

c. must always be equal to 0.

d. must always be equal to 1.

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c

Two events with nonzero probabilities

a. can not be both mutually exclusive and independent.

b. are always independent.

c. are always mutually exclusive.

d. can be both mutually exclusive and independent.

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a

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =

a. 0.00.

b. 0.15.

c. 0.20.

d. 0.30.

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a

A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial

a. tail can not appear.

b. head has a larger chance of appearing than tail.

c. tail has same chance of appearing as the head.

d. tail has a better chance of appearing than head.

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c

A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the

a. objective method.

b. experimental method.

c. subjective method.

d. classical method.

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d

If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A | B) =

a. 0.45

b. 0.40

c. 0.22

d. 0.00

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b

The sample space refers to

a. the sample size minus one.

b. any particular experimental outcome.

c. an event.

d. the set of all possible experimental outcomes.

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d

Two events are mutually exclusive

a. if most of their sample points are in common.

b. if their intersection is 0.5.

c. if their intersection is 1.

d. if they have no sample points in common.

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d

The intersection of two mutually exclusive events

a. must always be equal to 1.

b. must always be equal to 0.

c. can be any value between 0 to1.

d. can be any positive value.

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b

If X and Y are mutually exclusive events with P(A) = 0.295, P(B) = 0.32, then P(A | B) =

a. 0.6150.

b. 0.0000.

c. 1.0000.

d. 0.0944.

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b

In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The union of A and B is

a. all new customers.

b. all accounts from new customers and all accounts that are from 31 to 60 days past due.

c. all new customers whose accounts are between 31 and 60 days past due.

d. all accounts fewer than 31 or more than 60 days past due.

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b

Let F be the event that a customer is dissatisfied with the food at a restaurant and let S be the event that a customer is dissatisfied with the service. If P(F) = .15, P(S) = .40, and P(F ∩ S) = .10, what is the probability that a customer is dissatisfied with either the service or the food?

a. .65

b. .45

c. .55

d. .10

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b

The complement of P(A | B) is

a. P(A | BC).

b. P(B | A).

c. P(A I B).

d. P(AC | B).

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d

Each individual outcome of an experiment is called

a. a trial.

b. a sample point.

c. the sample space.

d. an event.

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b

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

a. 4/52

b. 1/52

c. 2/52

d. 3/52

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c

If P(A) = 0.62, P(B) = 0.56, and P(A ∪ B) = 0.70, then P(B | A) =

a. .9032.

b. .7742.

c. .4800.

d. .3472.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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Solution

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b

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

a. 0.59.

b. 0.43.

c. 0.75.

d. 0.14.

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b

A description of the distribution of the values of a random variable and their associated probabilities is called a

a. probability distribution.

b. table of binomial probability.

c. empirical discrete distribution.

d. bivariate distribution.

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a

The expected value for a binomial distribution is given by equation

a. n(1 - p).

b. np.

c. (n - 1)(1 - p).

d. (n - 1)p.

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b

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that the sample contains 2 female voters is

a. 0.0778

b. 0.3456

c. 0.7780

d. 0.5000

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b

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample exactly two are female?

a. 0.0007

b. 0.2936

c. 0.0413

d. 0.0896

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c

A weighted average of the values of a random variable, where the probability function provides weights, is known as

a. the probable value.

b. the median value.

c. the variance.

d. the expected value.

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d

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the

a. exponential probability distribution.

b. hypergeometric probability distribution.

c. binomial probability distribution.

d. Poisson probability distribution.

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b

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a. 0.0142

b. 0.7408

c. 0.9588

d. 0.2592

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Solution

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a

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions' properties are satisfied by random variable x?

a. Binomial

b. Hypergeometric

c. Normal

d. Poisson

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d

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

a. mixed type random variable.

b. multivariate random variable.

c. discrete random variable.

d. continuous random variable.

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d

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

a. Poisson distribution.

b. Uniform distribution.

c. Binomial distribution.

d. Normal distribution.

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a

Assume the number of customers who order a dessert with their meal on a given night at a local restaurant has the probability distribution given below.

The variance for the random variable x is _____.

a. .36

b. .60

c. 4

d. .77

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b

The following represents the probability distribution for the daily demand of computers at a local store.

Demand	Probability
0	0.1
1	0.2
2	0.3
3	0.2
4	0.2

The expected daily demand is

a. 2.0

b. 4.0

c. 2.2

d. 1.0

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c

In a binomial experiment

a. the probability changes from trial to trial.

b. the probability could change from trial to trial, depending on the situation under consideration.

c. the probability does not change from trial to trial.

d. the probability could change depending on the number of outcomes.

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c

In a binomial experiment

a. the probability changes from trial to trial.

b. the probability could change from trial to trial, depending on the situation under consideration.

c. the probability does not change from trial to trial.

d. the probability could change depending on the number of outcomes.

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c

In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is

a. 5

b. 6

c. 2

d. 10

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b

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.

Production
Per Month	Probability
1	0.01
2	0.04
3	0.10
4	0.80
5	0.05

The expected monthly production level is

a. 3.84

b. 3.00

c. 1.00

d. 4.00

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a

In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,

a. μ = 4, x = 3

b. μ = 3, x = 4

c. μ = 2, x = 3

d. μ = 1, x = 4

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c

The expected value for a binomial distribution is given by equation

a. np.

b. n(1 - p).

c. (n - 1)(1 - p).

d. (n - 1)p.

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A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

a. 0.10

b. 0.0004

c. 0.02

d. 0.0038

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d

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

a. 0.10

b. 0.0004

c. 0.02

d. 0.0038

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d

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

a. 16.

b. 20.

c. 4.

d. 2.

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Solution

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c

The probability distribution for the number of goals the Lions soccer team makes per game is given below.

	Number of Goals	Probability
	0	0.05
	1	0.15
	2	0.35
	3	0.30
	4	0.15

What is the probability that in a given game the Lions will score less than 3 goals?

a. .55

b. .85

c. .45

d. .80

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Solution

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a

In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,

a. μ = 2, x = 3

b. μ = 4, x = 3

c. μ = 1, x = 4

d. μ = 3, x = 4

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Solution

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a

The variance Var(x) for the binomial distribution is given by equation

a. np(1 - np).

b. n(1 - p).

c. np(n - 1).

d. np(1 - p).

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d

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

a. discrete random variable.

b. multivariate random variable.

c. continuous random variable.

d. mixed type random variable.

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are less than 3 occurrences is

a. .1239

b. .1016

c. .0659

d. .0948

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b

An air traffic controller has noted that it clears an average of seven planes per hour for landing. What is the probability that during the next two hours exactly 15 planes will be cleared for landing?

a. .0033

b. .0651

c. .0989

d. Not enough information is given to answer the question.

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c

The number of vehicle thefts in the parking lot of a shopping mall varies from month to month. Assume that the number of thefts (x) at the shopping mall has the following probability distribution.

The mean number of thefts per month is _____.

a. 6

b. .175

c. .70

d. 1.5

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Solution

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c

The number of vehicle thefts in the parking lot of a shopping mall varies from month to month. Assume that the number of thefts (x) at the shopping mall has the following probability distribution.

The mean number of thefts per month is _____.

a. 6

b. .175

c. .70

d. 1.5

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Solution

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c

Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0?

a. .6667

b. .0667

c. .0001

d. .9333

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b

The Poisson probability distribution is a

a. continuous probability distribution.

b. normal probability distribution.

c. discrete probability distribution.

d. uniform probability distribution.

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Solution

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c

In a Poisson probability problem, the rate of defects is one every two hours. To find the probability of three defects in four hours,

a. μ = 2, x = 3

b. μ = 4, x = 3

c. μ = 1, x = 4

d. μ = 3, x = 4

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a

A binomial probability distribution with p = .3 is

a. positively skewed.

b. multi-modal.

c. symmetric.

d. negatively skewed.

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Solution

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a

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a. 0.2592

b. 0.0142

c. 0.9588

d. 0.7408

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Solution

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b

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

a. multivariate random variable.

b. mixed type random variable.

c. discrete random variable.

d. continuous random variable.

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d

The probability distribution for the daily sales at Michael's Co. is given below.

Daily Sales (In $1,000s)	Probability
40	0.1
50	0.4
60	0.3
70	0.2

The probability of having sales of at least $50,000 is

a. 0.5

b. 0.90

c. 0.10

d. 0.30

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Solution

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b

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.

Production
Per Month	Probability
1	0.01
2	0.04
3	0.10
4	0.80
5	0.05

The expected monthly production level is

a. 4.00

b. 1.00

c. 3.84

d. 3.00

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Solution

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c

Which of the following is not a required condition for a discrete probability function?

a. Σf(x) = 0

b. Σf(x) = 1

c. f(x) ≥ 0 for all values of x

d. All of these choices are correct.

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a

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Which of the following discrete probability distributions' properties are satisfied by random variable x?

a. Poisson

b. Binomial

c. Hypergeometric

d. Normal

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a

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.

	x	f(x)
	0	0.80
	1	0.15
	2	0.04
	3	0.01

The mean and the standard deviation for the number of electrical outages (respectively) are

a. 3 and 0.01

b. 0.26 and 0.577

c. 2.6 and 5.77

d. 0 and 0.8

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b

The expected value for a binomial distribution is given by equation

a. np.

b. n(1 - p).

c. (n - 1)p.

d. (n - 1)(1 - p).

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Solution

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a

Using a hypergeometric distribution with N = 6 and r = 2, what is the probability for n = 4 and x = 0?

a. .9333

b. .6667

c. .0667

d. .0001

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The appropriate probability distribution for the random variable is

a. continuous.

b. either discrete or continuous depending on how the interval is defined.

c. discrete.

d. binomial.

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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Solution

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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Solution

Correct Response

c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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c

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

a. .9107

b. .0241

c. .0771

d. .1126

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c

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. .5

b. .025

c. .05

d. 0

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a

The uniform distribution defined over the interval from 25 to 40 has the probability density function

a. f(x) = 1/25 for 0 ≤ x ≤ 25 and f(x) = 1/40 for 26 ≤ x ≤ 40

b. f(x) = 1/15 for 25≤ x ≤ 40 and f(x) = 0 elsewhere

c. f(x) = 5/8 for 25 ≤ x ≤ 40 and f(x) = 0 elsewhere

d. f(x) = 1/40 for all x

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b

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

a. 50%

b. 38.49%

c. 38.59%

d. 76.98%

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d

For a continuous random variable x, the height of the function at x is

a. a value less than zero.

b. the probability at a given value of x.

c. 0.50, since it is the middle value.

d. named the probability density function f(x).

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d

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

a. 100.00

b. 90.51

c. 88.51

d. 93.2

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c

Suppose that the lifetime of batteries in a flashlight is exponentially distributed with a mean of 35 hours. What is the probability that the batteries will last between 25 and 30 hours?

a. .4244

b. .0651

c. .5105

d. .5756

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b

Joe's Record World has two stores and sales at each store follow a normal distribution. For store 1, μ = $2,000 and σ = $200 per day; for store 2, μ = $1,900 and σ = $300 per day. Which store is more likely to have a day's sales in excess of $2200?

a. Store 1 and store 2 are equally likely

b. Store 1

c. Store 2

d. More information is needed

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a

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in less than 6 minutes is

a. 1

b. 0.15

c. zero

d. 0.50

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c

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing less than 250 pounds is

a. 0.4772

b. 0.5000

c. 0.9772

d. 0.0528

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c

The probability density function for a uniform distribution ranging between 2 and 6 is

a. any positive value.

b. undefined.

c. 4.

d. 0.25.

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d

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

a. 0.0016

b. 0.0160

c. 0.1600

d. 0.9452

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d

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.

a. 30

b. 235

c. .03

d. 75

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b

The standard deviation of a normal distribution

a. is always 0.

b. is always 1.

c. cannot be negative.

d. can be any value.

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c

Which of the following distributions is not symmetric?

a. Normal

b. Exponential

c. Standard normal

d. All of these choices are symmetric.

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b

A binomial probability distribution has p = 0.15 and n = 200. What is the probability of 20 to 25 successes?

a. 0.17

b. 0.08

c. 0.10

d. 0.95

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a

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?

a. -2.06

b. -1.97

c. 3.06

d. 0.4803

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a

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?

a. -2.06

b. -1.97

c. 3.06

d. 0.4803

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a

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?

a. -2.06

b. -1.97

c. 3.06

d. 0.4803

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a

Which of the following distributions is not symmetric?

a. Normal

b. Exponential

c. Standard normal

d. All of these choices are symmetric.

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b

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

a. 8.53%

b. 18.53%

c. 0.853%

d. 91.47%

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a

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.

a. 30

b. 235

c. .03

d. 75

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b

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .05

c. .025

d. .5

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d

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .05

c. .025

d. .5

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d

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .05

c. .025

d. .5

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d

Find P(10 ≤ x ≤ 30) for a uniform random variable defined on the interval 0 to 40.

a. 0

b. .05

c. .025

d. .5

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d    

A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000?

a. .9999

b. .9115

c. .5000

d. .0885

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d

The probability distribution that can be described by just one parameter is the

a. binomial.

b. exponential.

c. uniform.

d. normal.

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b

The probability distribution that can be described by just one parameter is the

a. binomial.

b. exponential.

c. uniform.

d. normal.

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b

The probability distribution that can be described by just one parameter is the

a. binomial.

b. exponential.

c. uniform.

d. normal.

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b

The probability distribution that can be described by just one parameter is the

a. binomial.

b. exponential.

c. uniform.

d. normal.

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b

The probability distribution that can be described by just one parameter is the

a. binomial.

b. exponential.

c. uniform.

d. normal.

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b

A normal distribution with a mean of 0 and a standard deviation of 1 is called

a. a probability density function.

b. a standard normal distribution.

c. exponential probability distribution.

d. uniform probability distribution.

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b

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

a. 18.53%

b. 0.853%

c. 8.53%

d. 91.47%

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c

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370?

a. 1.50

b. – 1.53

c. 1.96

d. .8264

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b

Let x be a uniform random variable on the interval 1 ≤ x ≤ 6. What is the standard deviation of x?

a. 2.08

b. 1.44

c. .2

d. 3.5

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b

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

a. 0.1600

b. 0.0016

c. 0.9452

d. 0.0160

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c

For a uniform probability density function,

a. the height of the function is the same for each value of x.

b. the height of the function cannot be larger than one.

c. the height of the function is different for various values of x.

d. the height of the function decreases as x increases.

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a

 Which of the following is not a characteristic of the normal probability distribution?

a. The mean of the distribution can be negative, zero, or positive

b. The standard deviation must be 1

c. The mean, median, and the mode are equal

d. The distribution is symmetrical

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b

What is the mean of x, given the function below?

f(x) =(1/10) e-x/10    x ≥ 0

a. 100

b. 0.10

c. 10

d. 1,000

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c

What is the mean of x, given the function below?

f(x) =(1/10) e-x/10    x ≥ 0

a. 100

b. 0.10

c. 10

d. 1,000

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c

For the standard normal probability distribution, the area to the right of the mean is

a. 1.96.

b. 3.09.

c. 1.

d. 0.5.

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d

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

a. different for each interval.

b. zero.

c. the same for each interval.

d. at least one.

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c

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.5?

a. 1.0000

b. 0.1915

c. 0.3413

d. 0.0000

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d

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

a. 50%

b. 1.96%

c. 21%

d. It could be any value, depending on the magnitude of the standard deviation

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a

z is a standard normal random variable. The P(1.05 ≤ z ≤ 2.13) equals

a. 0.4834

b. 0.3531

c. 0.8365

d. 0.1303

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d

A value of 0.5 that is added to and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

a. factor of conversion.

b. probability density factor.

c. continuity approximation factor.

d. continuity correction factor.

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d

For a normal distribution, a negative value of z indicates

a. the area corresponding to the z is negative.

b. the z is to the left of the mean.

c. the z is to the right of the mean.

d. a mistake has been made in computations, because z is always positive.

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b

For a normal distribution, a negative value of z indicates

a. the area corresponding to the z is negative.

b. the z is to the left of the mean.

c. the z is to the right of the mean.

d. a mistake has been made in computations, because z is always positive.

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b

For a normal distribution, a negative value of z indicates

a. the area corresponding to the z is negative.

b. the z is to the left of the mean.

c. the z is to the right of the mean.

d. a mistake has been made in computations, because z is always positive.

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b

For a normal distribution, a negative value of z indicates

a. the area corresponding to the z is negative.

b. the z is to the left of the mean.

c. the z is to the right of the mean.

d. a mistake has been made in computations, because z is always positive.

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b

Let F be the event that a customer is dissatisfied with the food at a restaurant and let S be the event that a customer is dissatisfied with the service. If P(F) = .15, P(S) = .40, and P(F ∩ S) = .10, what is the probability that a customer is dissatisfied with either the service or the food?

a. .55

b. .45

c. .65

d. .10

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b

The collection of all possible sample points in an experiment is

a. a combination.

b. the sample space.

c. the population.

d. an event.

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b

If A and B are independent events with P(A) = .1 and P(B) = .4, then

a. P(A ∩ B) = .04.

b. P(A ∩ B) = .25.

c. P(A ∪ B) = .5.

d. P(A ∩ B) = 0.

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a

If P(A) = 0.75, P(A ∪ B) = 0.86, and P(A ∩ B) = 0.56, then P(B) =

a. 0.67.

b. 0.56.

c. 0.25.

d. 0.11.

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a

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?

a. 64

b. 4

c. 32

d. 16

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a

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for combinations.

c. counting rule for independent events.

d. counting rule for permutations.

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b

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for combinations.

c. counting rule for independent events.

d. counting rule for permutations.

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Solution

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b

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for combinations.

c. counting rule for independent events.

d. counting rule for permutations.

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Solution

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b

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for combinations.

c. counting rule for independent events.

d. counting rule for permutations.

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Solution

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b

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

a. counting rule for multiple-step experiments.

b. counting rule for combinations.

c. counting rule for independent events.

d. counting rule for permutations.

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Solution

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b

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

a. Binomial distribution.

b. Poisson distribution.

c. Normal distribution.

d. Uniform distribution.

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b

he random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are less than 3 occurrences is

a. .0659

b. .1239

c. .0948

d. .1016

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d

he random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are less than 3 occurrences is

a. .0659

b. .1239

c. .0948

d. .1016

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d

Random variable x has the probability function: f(x) = x/6 for x = 1,2 or 3. The expected value of x is

a. 2.333

b. 0.500

c. 0.333

d. 2.000

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a

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.

Production
Per Month	Probability
1	0.01
2	0.04
3	0.10
4	0.80
5	0.05

The expected monthly production level is

a. 4.00

b. 3.00

c. 1.00

d. 3.84

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d

Which of the following is not a required condition for a discrete probability function?

a. Σf(x) = 0

b. Σf(x) = 1

c. f(x) ≥ 0 for all values of x

d. All of these choices are correct.

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a

Which of the following is not a required condition for a discrete probability function?

a. Σf(x) = 0

b. Σf(x) = 1

c. f(x) ≥ 0 for all values of x

d. All of these choices are correct.

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a

The following represents the probability distribution for the daily demand of computers at a local store.

Demand	Probability
0	0.1
1	0.2
2	0.3
3	0.2
4	0.2

The probability of having a demand for at least two computers is

a. 0.7

b. 0.4

c. 0.3

d. 1.0

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a

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The variance of x equals

a. 85

b. 9.165

c. 93.33

d. 84

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d

Consider the probability distribution below.

x	f(x)
10	.2
20	.3
30	.4
40	.1

The variance of x equals

a. 85

b. 9.165

c. 93.33

d. 84

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d

The mean of a standard normal probability distribution

a. can be any value as long as it is positive.

b. can be any value.

c. is always equal to zero.

d. is always greater than zero.

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c

The probability density function for a uniform distribution ranging between 2 and 6 is

a. 4.

b. undefined.

c. any positive value.

d. 0.25.

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Solution

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d

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

a. 0.4772

b. 0.0228

c. 0.9772

d. 0.5000

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c

Suppose the flight time between Atlanta and Salt Lake City is uniformly distributed on the interval from 220 to 250 minutes. The expected flight time (in minutes) is _____.

a. 30

b. .03

c. 235

d. 75

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c

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

A standard normal distribution is a normal distribution with

a. any mean and a standard deviation of 1.

b. a mean of 0 and standard deviation of 1.

c. a mean of 0 and a standard deviation of 0.

d. a mean of 1 and a standard deviation of 1.

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b

Posterior probabilities are computed using

a. Chebyshev's theorem.

b. the empirical rule.

c. relative frequency.

d. Bayes' theorem.

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d

A graphical method of representing the sample points of an experiment is a

a. dot plot.

b. stem-and-leaf display.

c. stacked bar chart.

d. tree diagram.

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d

Which of the following statements is always true?

a. P(A) + P(B) = 1

b. ∑P ≥ 1

c. -1 ≤ P(Ei) <≤ 1

d. P(A) = 1 - P(Ac)

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d

Events that have no sample points in common are

a. complements.

b. posterior events.

c. independent events.

d. mutually exclusive events.

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d

If a coin is tossed three times, the likelihood of obtaining three heads in a row is

a. 0.500.

b. 0.875.

c. 0.125.

d. 0.0.

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c

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. complements of each other.

b. independent events.

c. non-mutually exclusive.

d. mutually exclusive.

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d

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

a. 0.

b. larger than the probability of tails.

c. 1/2.

d. 1/16.

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c

The intersection of two mutually exclusive events

a. can be any value between 0 to1.

b. must always be equal to 1.

c. can be any positive value.

d. must always be equal to 0.

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d

In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event B mean the account is that of a new customer. The intersection of A and B is

a. all accounts fewer than 31 or more than 60 days past due.

b. all accounts from new customers and all accounts that are from 31 to 60 days past due.

c. all new customers.

d. all new customers whose accounts are between 31 and 60 days past due.

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d

Initial estimates of the probabilities of events are known as

a. posterior probabilities.

b. conditional probabilities.

c. prior probabilities.

d. subjective probabilities.

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c

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

a. 6.

b. 2.

c. 8.

d. 4.

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c

An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is

a. 0.100.

b. 0.024.

c. 0.900.

d. 0.500.

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a

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the

a. subjective method.

b. posterior method.

c. classical method.

d. relative frequency method.

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d

If P(A) = 0.7, P(B) = 0.6, P(A ∩ B) = 0, then events A and B are

a. mutually exclusive.

b. non-mutually exclusive.

c. complements of each other.

d. independent events.

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Solution

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a

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

a. 8.

b. 2.

c. 4.

d. 16.

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d

If P(A) = 0.50, P(B) = 0.40 and P(A ∪ B) = 0.88, then P(B |A) =

a. 0.03.

b. 0.02.

c. 0.04.

d. 0.05.

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c

The prior probabilities for events A1 and A2 are P(A1) = .25 and P(A2) = .75. The conditional probabilities of event B given A1 and A2 are P(B | A1) = .45, and P(B | A2) = .30. Using Bayes' theorem, what is the posterior probability P(A2 | B)?

a. .667

b. .775

c. .225

d. .338

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a

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

a. 16

b. 2

c. 4

d. 12

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a

The union of events A and B is the event containing all the sample points belonging to

a. A or B or both.

b. B or A.

c. A or B, but not both.

d. A or B.

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a

A six-sided die is tossed 3 times. The probability of observing three ones in a row is

a. 1/6.

b. 1/216.

c. 3/6.

d. 1/27.

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b

If A and B are independent events with P(A) = .1 and P(B) = .4, then

a. P(A ∩ B) = .25.

b. P(A ∩ B) = .04.

c. P(A ∪ B) = .5.

d. P(A ∩ B) = 0.

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Solution

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b