Chapter 5 Quiz Solutions
1. 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 expected value of the random variable x is
a. 2.30.
b. 5.3.
c. 2.
d. 10.
Correct Response :b
2. The use of the relative frequency method to develop discrete probability distributions leads to what is called a
a. empirical discrete distribution.
b. non-uniform discrete distribution.
c. uniform discrete distribution.
d. binomial discrete distribution.
Correct Response: a
3. The binomial probability distribution is used with
a. a uniform random variable.
b. a discrete random variable.
c. a continuous random variable.
d. an intermittent random variable.
Correct Response:b
4. 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. 10
c. 6
d. 2
Correct Response:c
5. Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is
a. 12
b. 20
c. 2.83
d. 3.46
Correct Response:a
6. 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. discrete.
b. continuous.
C. binomial.
d. either discrete or continuous depending on how the interval is defined.
Correct Response: a
7. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
a. The experiment has a sequence of n identical trials
b. The probabilities of the outcomes do not change from one trial to another
c. Exactly two outcomes are possible on each trial
d. The trials are dependent
Correct Response:d
8. Consider the probability distribution below.
x f(x)
10 .2
20 .3
30 .4
40 .1
The variance of x equals
a. 93.33
b. 85
c. 84
d. 9.165
Correct Response: c
9. Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?
a. The trials are dependent on each other
b. The experiment has at least two possible outcomes
c. Exactly two outcomes are possible on each trial
d. The probabilities of the outcomes changes from one trial
Correct Response: c
10. In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?
a. 0.0600
b. 0.2800
c. 0.0036
d. 0.0555
Correct Response: d
11, The variance Var(x) for the binomial distribution is given by equation
a. np(1 - p).
b. np(n - 1).
c. n(1 - p).
d. np(1 - np).
Correct Response: a
12. The Poisson probability distribution is a
a. uniform probability distribution.
b. normal probability distribution.
c. continuous probability distribution.
d. discrete probability distribution.
Correct Response: d
13. A random variable that may take on any value in an interval or collection of intervals is known as a
a. discrete random variable.
b. mixed type random variable.
c. continuous random variable.
d. multivariate random variable.
Correct Response: c
14. Which of the following is a required condition for a discrete probability function?
a. ∑f(x) = 1 for all values of x
b. ∑f(x) ≥ 1 for all values of x
c. f(x) ≤ 0 for all values of x
d. ∑f(x) = 0 for all values of x
Correct Response: a
15. 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. 0.90
b. 0.30
c. 0.10
d. 0.5
Correct Response: a
16. Which of the following is a required condition for a discrete probability function?
a. f(x) ≥ 1 for all values of x
b. ∑f(x) = 1 for all values of x
c. ∑f(x) = 0 for all values of x
d. f(x) < 0 for all values of x
Correct Response: b
17. Experiments with repeated independent trials will be described by the binomial distribution if
a. the time between trials is constant.
b. each trial has exactly two outcomes whose probabilities do not change.
c. each trial result influences the next.
d. the trials are continuous.
Correct Response: b
18. Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.
a. continuous
b. intermittent
c. uniform
d. discrete
Correct Response: a
19. 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 6 are male?
a. 0.0007
b. 0.0079
c. 0.0499
d. 0.0413
Correct Response: c
20. 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. 4.00
c. 3.00
d. 3.84
Correct Response: d
1. 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 expected value of the random variable x is
a. 2.30.
b. 5.3.
c. 2.
d. 10.
Correct Response :b
2. The use of the relative frequency method to develop discrete probability distributions leads to what is called a
a. empirical discrete distribution.
b. non-uniform discrete distribution.
c. uniform discrete distribution.
d. binomial discrete distribution.
Correct Response: a
3. The binomial probability distribution is used with
a. a uniform random variable.
b. a discrete random variable.
c. a continuous random variable.
d. an intermittent random variable.
Correct Response:b
4. 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. 10
c. 6
d. 2
Correct Response:c
5. Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is
a. 12
b. 20
c. 2.83
d. 3.46
Correct Response:a
6. 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. discrete.
b. continuous.
C. binomial.
d. either discrete or continuous depending on how the interval is defined.
Correct Response: a
7. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?
a. The experiment has a sequence of n identical trials
b. The probabilities of the outcomes do not change from one trial to another
c. Exactly two outcomes are possible on each trial
d. The trials are dependent
Correct Response:d
8. Consider the probability distribution below.
x f(x)
10 .2
20 .3
30 .4
40 .1
The variance of x equals
a. 93.33
b. 85
c. 84
d. 9.165
Correct Response: c
9. Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?
a. The trials are dependent on each other
b. The experiment has at least two possible outcomes
c. Exactly two outcomes are possible on each trial
d. The probabilities of the outcomes changes from one trial
Correct Response: c
10. In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials?
a. 0.0600
b. 0.2800
c. 0.0036
d. 0.0555
Correct Response: d
11, The variance Var(x) for the binomial distribution is given by equation
a. np(1 - p).
b. np(n - 1).
c. n(1 - p).
d. np(1 - np).
Correct Response: a
12. The Poisson probability distribution is a
a. uniform probability distribution.
b. normal probability distribution.
c. continuous probability distribution.
d. discrete probability distribution.
Correct Response: d
13. A random variable that may take on any value in an interval or collection of intervals is known as a
a. discrete random variable.
b. mixed type random variable.
c. continuous random variable.
d. multivariate random variable.
Correct Response: c
14. Which of the following is a required condition for a discrete probability function?
a. ∑f(x) = 1 for all values of x
b. ∑f(x) ≥ 1 for all values of x
c. f(x) ≤ 0 for all values of x
d. ∑f(x) = 0 for all values of x
Correct Response: a
15. 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. 0.90
b. 0.30
c. 0.10
d. 0.5
Correct Response: a
16. Which of the following is a required condition for a discrete probability function?
a. f(x) ≥ 1 for all values of x
b. ∑f(x) = 1 for all values of x
c. ∑f(x) = 0 for all values of x
d. f(x) < 0 for all values of x
Correct Response: b
17. Experiments with repeated independent trials will be described by the binomial distribution if
a. the time between trials is constant.
b. each trial has exactly two outcomes whose probabilities do not change.
c. each trial result influences the next.
d. the trials are continuous.
Correct Response: b
18. Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.
a. continuous
b. intermittent
c. uniform
d. discrete
Correct Response: a
19. 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 6 are male?
a. 0.0007
b. 0.0079
c. 0.0499
d. 0.0413
Correct Response: c
20. 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. 4.00
c. 3.00
d. 3.84
Correct Response: d
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