Exhibit 1-2
In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the president is doing his job.
Refer to Exhibit 1-2. A political pollster states, "Forty five percent of all voters approve of the president." This statement is an example of _____.
Select one:
a. descriptive statistics
b. statistical inference
c. a population
d. a sample
b. statistical inference
The birth weight of newborns, measured in grams, is an example of:
Quantitative data
In a recent study based upon an inspection of 200 homes in Daisy City, 120 were found to violate one or more city codes.
Refer to Exhibit 1-1. The city manager released a statement that 60% of Daisy City's 3,000 homes are in violation of city codes. The manager's statement is an example of _____.
In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the president is doing his job.
Refer to Exhibit 1-2. The 45% approval is an example of _____.
In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the president is doing his job.
Refer to Exhibit 1-2. A political pollster states, "Forty five percent of all voters approve of the president." This statement is an example of _____.
The graph below best exemplifies a _____.
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The cumulative frequency for the class of 11−15 is _____.
Information on the type of industry is provided for a sample of 50 Fortune 500 companies
| Industry Type | Frequency | ||
| Banking | 7 | ||
| Consumer Products | 15 | ||
| Electronics | 10 | ||
| Retail | 18 | ||
The relative frequency of industries that are classified as banking is _____.
The numbers of hours worked (per week) by 400 statistics students are shown below.
| Number of Hours | Frequency | |||
| 0 ≤ x < 10 | 20 | |||
| 10 ≤ x < 20 | 80 | |||
| 20 ≤ x < 30 | 200 | |||
| 30 ≤ x < 40 | 100 | |||
The class width for this distribution _____.
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The number of workers who took at least 11 sick days per month is _____.
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The cumulative frequency for the class of 11−15 is _____.
A survey of 400 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 | Other | Total | ||
| Yes | 35 | 42 | 63 | 140 | ||
| No | 91 | 104 | 65 | 260 | ||
| Total | 126 | 146 | 128 | 400 | ||
Of those students who are majoring in Business, what percentage plans to go to graduate school?
Information on the type of industry is provided for a sample of 50 Fortune 500 companies
| Industry Type | Frequency | ||
| Banking | 7 | ||
| Consumer Products | 15 | ||
| Electronics | 10 | ||
| Retail | 18 | ||
The number of industries that are classified as retail is _____.
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The midpoint of the first class is _____.
A survey of 400 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 | Other | Total | ||
| Yes | 35 | 42 | 63 | 140 | ||
| No | 91 | 104 | 65 | 260 | ||
| Total | 126 | 146 | 128 | 400 | ||
What percentage of the students' undergraduate major is Engineering?
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The relative frequency of workers who took 10 or fewer sick days is _____.
In a class with 30 students, we ask, "If you could have any super power, what would it be?" Each student could only choose one super power. The resulting pie chart is below. The most popular choice of super power was _____.
The numbers of hours worked (per week) by 400 statistics students are shown below.
| Number of Hours | Frequency | |||
| 0 ≤ x < 10 | 20 | |||
| 10 ≤ x < 20 | 80 | |||
| 20 ≤ x < 30 | 200 | |||
| 30 ≤ x < 40 | 100 | |||
The percentage of students working less than 20 hours is _____.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 55 | |||
| 11 − 15 | 13 | |||
| 16 − 20 | 12 | |||
The cumulative percent frequency for the class of 16−20 is _____.
| Number of Days | Frequency | |||
| 0 − 5 | 110 | |||
| 6 − 10 | 70 | |||
| 11 − 15 | 13 | |||
| 16 − 20 | 7 | |||
The number of workers who took at least 11 sick days per month is _____.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 55 | |||
| 11 − 15 | 13 | |||
| 16 − 20 | 12 | |||
The cumulative percent frequency for the class of 16−20 is _____.
| Industry Type | Frequency | ||
| Banking | 9 | ||
| Consumer Products | 12 | ||
| Electronics | 12 | ||
| Retail | 17 | ||
The number of industries that are classified as retail is _____.
What type of phone do males prefer?
The number of sick days taken (per month) by 200 factory workers is summarized below.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 14 | |||
| 16 − 20 | 1 | |||
The number of workers who took less than 11 sick days per month is _____.
| Number of Days | Frequency | |||
| 0 − 5 | 120 | |||
| 6 − 10 | 65 | |||
| 11 − 15 | 13 | |||
| 16 − 20 | 2 | |||
The number of workers who took more than 10 sick days per month is _____.
A researcher has collected the following sample data. The mean of the sample is 5.
| 3 | 5 | 12 | 3 | 2 |
The standard deviation is _____.
| 6 | 10 | 16 | 2 | 6 |
The variance is _____.
A researcher has collected the following sample data. The mean of the sample is 5.
| 3 | 5 | 12 | 3 | 2 |
The interquartile range is _____.
A researcher has collected the following sample data. The mean of the sample is 5.
| 3 | 5 | 12 | 3 | 2 |
The interquartile range is _____.
A researcher has collected the following sample data. The mean of the sample is 5.
| 3 | 5 | 12 | 3 | 2 |
The standard deviation is _____.
| 5 | 6 | 11 | 8 | 5 |
The interquartile range is _____.
| 6 | 13 | 7 | 9 | 6 |
| 7 | 8 | 6 | 13 | 5 |
The 75th percentile is _____.
Suppose annual salaries for sales associates from Hayley's Heirlooms have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500.
The z-score for a sales associate from this store who earns $28,000 is _____.
| 7 | 14 | 8 | 10 | 7 |
| 8 | 9 | 7 | 14 | 6 |
The mode is _____.
| 7 | 7 | 13 | 5 | 3 |
The standard deviation is _____.
| 7 | 14 | 8 | 10 | 7 |
| 8 | 9 | 7 | 14 | 6 |
The mean is _____.
| Speed (mph) | Frequency | |
| 50−54 | 1 | |
| 55−59 | 4 | |
| 60−64 | 5 | |
| 65−69 | 10 | |
| 70−74 | 7 | |
| 75−79 | 8 | |
| 35 | ||
The mean is _____.
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An
experiment has three steps with three outcomes possible for the first step,
two outcomes possible for the second step, and four outcomes possible for the
third step. How many experimental outcomes exist for the entire experiment?
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How
many permutations of three items can be selected from a group of six? Use
the letters , , , , , and to identify the
items, and list each of the permutations of items , , and .
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A
decision maker subjectively assigned the following probabilities to the four
outcomes of an experiment: , , , and . Are these
probability assignments valid? Explain.
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A
CBS News/New York Times poll of adults in the United
States asked the question, "Do you think global warming will have an
impact on you during your lifetime?" (CBS News website). Consider the
responses by age groups shown below.
a. What is the probability that a
respondent - years of age thinks that global warming will not have
an impact during his/her lifetime (to decimals)? b. What is the probability that a
respondent + years of age thinks that global warming will not have an
impact during his/her lifetime (to decimals)? c. For a randomly selected respondent,
what is the probability that a respondent answers yes
(to decimals)? d. Based on the survey results, does
there appear to be a difference between ages - and + regarding
concern over global warming?
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The
National Highway Traffic Safety Administration (NHTSA) collects traffic
safety-related data for the U.S. Department of Transportation. According to
NHTSA's data, fatal collisions in were the result of
collisions with fixed objects (NHTSA website, https://www.careforcrashvictims.com/wp-content/uploads/2018/07/Traffic-Safety-Facts-2016_-Motor-Vehicle-Crash-Data-from-the-Fatality-Analysis-Reporting-System-FARS-and-the-General-Estimates-System-GES.pdf).
The following table provides more information on these collisions.
Assume
that a collision will be randomly chosen from this population. Round your
answers to four decimal places. a. What is the probability of a fatal
collision with a pole or post? b. What is the probability of a fatal
collision with a guardrail? c. What type of fixed object is least
likely to be involved in a fatal collision? What
is the probability associated with this type of fatal collision? d. What type of object is most likely
to be involved in a fatal collision? What
is the probability associated with this type of fatal collision?
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A Pew
Research Center survey (Pew Research website) examined the use of social
media platforms in the United States. The survey found that there is
a probability that a randomly selected American will use Facebook
and a probability that a randomly selected American will use LinkedIn.
In addition, there is a probability that a randomly selected
American will use both Facebook and LinkedIn. a.
What is the probability that a
randomly selected person will use Facebook or LinkedIn
(to decimals)? b.
What is the probability that a
randomly selected person will not use either social media platform
(to decimals)?
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High
school seniors with strong academic records apply to the nation's most
selective colleges in greater numbers each year. Because the number of slots
remains relatively stable, some colleges reject more early applicants.
Suppose that for a recent admissions class, an Ivy League college
received applications for early admission. Of this group, it
admitted students early, rejected outright, and
deferred to the regular admissions pool for further consideration.
In the past, this school has admitted of the deferred early
admission applicants during the regular admission process. Counting the
students admitted early and the students admitted during the regular
admission process, the total class size was . Let , ,
and represent the events that a student who applies for early
admission is admitted early, rejected outright, or deferred to the regular
admissions pool. If
your answer is zero, enter "". a. Use the data to
estimate , , and (to decimals).
b. Are
events and mutually exclusive? Find (to decimals). c. For the students
who were admitted, what is the probability that a randomly selected student
was accepted for early admission (to decimals)? d. Suppose a student applies for
early admission. What is the probability that the student will be admitted
for early admission or be deferred and later admitted during the regular
admission process (to decimals)?
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Assume
that we have two events, and , that are mutually exclusive.
Assume further that we know and . If
an amount is zero, enter "". a. What is ? b. What is ? c. A student in statistics
argues that the concepts of mutually exclusive events and independent events
are really the same, and that if events are mutually exclusive they must be
independent. Do you agree with this statement? Use the probability
information in this problem to justify your answer. d. What general conclusion would
you make about mutually exclusive and independent events given the results of
this problem?
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To
better understand how husbands and wives feel about their finances, Money
Magazine conducted a national poll of married adults
age and older with household incomes of or more (Money website).
Consider the following example set of responses to the question, "Who is
better at getting deals?"
Round
your answers to four decimal places, if necessary. a.
Develop a joint probability table
and use it to answer the following questions.
b.
Construct the marginal
probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.
is
over twice as likely as either . c.
Given that the respondent is a
husband, what is the probability that he feels he is better at getting deals
than his wife? d.
Given that the respondent is a
wife, what is the probability that she feels she is better at getting deals
than her husband? e.
Given a response "My
spouse" is better at getting deals, what is the probability that the
response came from a husband? f.
Given a response "We are
equal," what is the probability that the response came from a husband? What
is the probability that the response came from a wife?
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A Pew
Research Center survey found that more Americans believe they could give up
their televisions than could give up their cell phones (Pew Research
website). Assume that the following table represents the joint probabilities
of Americans who could give up their television or cell phone. Excel
File: data04-37.xlsx
a. What is the probability that a
person could give up her cell phone (to decimals)? b. What is the probability that a
person who could give up her cell phone could also give up television (to decimals)? c. What is the probability that a
person who could not give up her cell phone could give up television
(to decimals)? d. Is the probability a person could
give up television higher if the person could not give up a cell phone or if the
person could give up a cell phone? The
probability a person could give up television if they could not give up a
cellphone is than
the probability a person could give up television if they could give up a
cellphone.
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A
consulting firm submitted a bid for a large research project. The firm's
management initially felt they had a chance of getting the
project. However, the agency to which the bid was submitted subsequently
requested additional information on the bid. Past experience indicates that
for of the successful bids and of the unsuccessful bids
the agency requested additional information. a. What is the prior probability
of the bid being successful (that is, prior to the request for additional information)
(to decimal)? b. What is the conditional
probability of a request for additional information given that the bid will
ultimately be successful (to decimals)? c. Compute the posterior
probability that the bid will be successful given a request for additional
information (to decimals).
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According
to a article in Esquire magazine,
approximately of males over age will develop cancerous
cells in their prostate. Prostate cancer is second only to skin cancer as the
most common form of cancer for males in the United States. One of the most
common tests for the detection of prostate cancer is the prostate-specific
antigen (PSA) test. However, this test is known to have a high false-positive
rate (tests that come back positive for cancer when no cancer is present).
Suppose there is a probability that a male patient has prostate
cancer before testing. The probability of a false-positive test is , and
the probability of a false-negative (no indication of cancer when cancer is
actually present) is .
a.
What is the probability that the
male patient has prostate cancer if the PSA test comes back positive
(to decimals)? b.
What is the probability that the
male patient has prostate cancer if the PSA test comes back negative
(to decimals)? c.
For older men, the prior
probability of having cancer increases. Suppose that the prior probability of
the male patient is rather than . What is the probability
that the male patient has prostate cancer if the PSA test comes back positive
(to decimals)? What
is the probability that the male patient has prostate cancer if the PSA test
comes back negative (to decimals)? d.
What can you infer about the PSA
test from the results of parts (a), (b), and (c)? The
difference between and in parts (a) and (b) is than
the difference between and in part (c).
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A
financial manager made two new investments—one in the oil industry and one in
municipal bonds. After a one-year period, each of the investments will be classified
as either successful or unsuccessful. Consider the making of the two
investments as an experiment. a. How many sample points exist
for this experiment? b. Choose a tree diagram.
c. Let and How
many sample points exist for ? How
many sample points exist for ? d. Identify the sample points in
the union of the events (). e. Identify the sample points in
the intersection of the events (). f. Are
events and mutually exclusive? Explain.
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A
study of hospital admissions in New York State found
that of the admissions led to treatment-caused injuries.
One-seventh of these treatment-caused injuries resulted in death, and
one-fourth were caused by negligence. Malpractice claims were filed in one
out of cases involving negligence, and payments were made in one
out of every two claims. a. What is the probability a
person admitted to the hospital will suffer a treatment-caused injury due to
negligence (to decimals)? b. What is the probability a
person admitted to the hospital will die from a treatmen-caused injury
(to decimals)? c. What is the probability a
person admitted to the hospital is paid a malpractice claim
(to decimals)?
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A
large consumer goods company ran a television advertisement for one of its
soap products. On the basis of a survey that was conducted, probabilities
were assigned to the following events. B = individual purchased the
product The
probabilities assigned were , , and a. What is the probability of an
individual’s purchasing the product given that the individual recalls seeing
the advertisement (to decimal)? Does
seeing the advertisement increase the probability that the individual will
purchase the product? As
a decision maker, would you recommend continuing the advertisement (assuming
that the cost is reasonable)? b. Assume that individuals who
do not purchase the company’s soap product buy from its competitors. What
would be your estimate of the company’s market share (to the nearest whole
number)? % Would
you expect that continuing the advertisement will increase the company's
market share? Why or why not? c. The company also tested
another advertisement and assigned it values of and . What
is for this other advertisement (to decimals)? Which
advertisement seems to have had the bigger effect on customer purchases?
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A
company studied the number of lost-time accidents occurring at its
Brownsville, Texas, plant. Historical records show that of the
employees suffered lost-time accidents last year. Management believes that a
special safety program will reduce such accidents to during the
current year. In addition, it estimates that of employees who had
lost-time accidents last year will experience a lost-time accident during the
current year. a. What percentage of the
employees will experience lost-time accidents in both years
(to decimals)? % b. What percentage of the
employees will suffer at least one lost-time accident over the two-year
period (to decimals)? %
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An
oil company purchased an option on land in Alaska. Preliminary geologic
studies assigned the following prior probabilities. a. What is the probability of
finding oil (to decimals)? b. After feet of
drilling on the first well, a soil test is taken. The probabilities of
finding the particular type of soil identified by the test are given below. Given
the soil found in the test, use Bayes' theorem to compute the following
revised probabilities (to decimals).
What
is the new probability of finding oil (to decimals)? According
to the revised probabilities, what is the quality of oil that is most likely
to be found?
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To
perform a certain type of blood analysis, lab technicians must perform two
procedures. The first procedure requires either one or two separate steps,
and the second procedure requires either one, two, or three steps. a. List the experimental
outcomes associated with performing the blood analysis. b. Let denote the
total number of steps required to do the complete analysis (both procedures).
Show what value of random variable will assume for each of the experimental
outcomes. (If an outcome does not occur, enter “0”.)
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A
technician services mailing machines at companies in the Phoenix area.
Depending on the type of malfunction, the service call can
take , , , or hours. The different types of
malfunctions occur at the same frequency. If
required, round your answers to two decimal places. a. Develop a probability
distribution for the duration of a service call.
b. Which of the following
probability distribution graphs accurately represents the data set?
c. Consider the required
conditions for a discrete probability function, shown below.
d. What is the probability a
service call will take hours? e. A service call has just come
in, but the type of malfunction is unknown. It is P.M. and service technicians usually get off at P.M. What is the probability the service technician will have to work
overtime to fix the machine today?
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A
psychologist determined that the number of sessions required to obtain the
trust of a new patient is either , , or . Let be a
random variable indicating the number of sessions required to gain the
patient's trust. The following probability function has been proposed. for or a. Consider the required
conditions for a discrete probability function, shown below.
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The
following table provides a probability distribution for the random
variable . Excel
File: data05-15.xlsx
a. Compute , the
expected value of .
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New
legislation passed in 2017 by the U.S. Congress changed tax laws that affect
how many people file their taxes in 2018 and beyond. These tax law changes
will likely lead many people to seek tax advice from their accountants (The
New York Times). Backen and Hayes LLC is an accounting firm in New York
state. The accounting firm believes that it may have to hire additional
accountants to assist with the increased demand in tax advice for the
upcoming tax season. Backen and Hayes LLC has developed the following
probability distribution for number of new clients seeking tax
advice. Excel
File: data05-19.xlsx
a.
Is this a valid probability
distribution? Explain.
b.
What is the probability that Backen
and Hayes LLC will obtain or more new clients (to 2 decimals)? c.
What is the probability that Backen
and Hayes LLC will obtain fewer than new clients (to 2 decimals)? d.
Compute the expected value,
variance, and standard deviation of (to 2 decimals).
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The
following probability distributions of job satisfaction scores for a sample
of information systems (IS) senior executives and middle managers range from
a low of (very dissatisfied) to a high of (very
satisfied). Excel
File: data05-21.xlsx
a. What is the expected value of the
job satisfaction score for senior executives (to 2 decimals)? b. What is the expected value of the
job satisfaction score for middle managers (to 2 decimals)? c. Compute the variance of job
satisfaction scores for executives and middle managers (to 2 decimals).
d. Compute the standard deviation of
job satisfaction scores for both probability distributions (to 2 decimals).
e. What comparison can you make about
the job satisfaction of senior executives and middle managers?
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J.
P. Morgan Asset Management publishes information about financial investments.
Between 2002 and 2011 the expected return for the
S&P was with a standard deviation of and
the expected return over that same period for a Core Bonds fund
was with a standard deviation of (J. P. Morgan Asset
Management, Guide to the Markets). The publication also reported
that the correlation between the S&P and Core Bonds is .
You are considering portfolio investments that are composed of an
S&P index fund and a Core Bonds fund. a.
Using the information provided,
determine the covariance between the S&P and Core Bonds. Round
your answer to two decimal places. If required enter negative values as
negative numbers. b.
Construct a portfolio that
is invested in an S&P index fund and in
a Core Bond fund. Let x represent the S&P 500 and y represent
the Core Bond fund. Round your answers to one decimal place. In
percentage terms, what is the expected return and standard deviation for such
a portfolio? Round your answers to two decimal places.
c.
Construct a portfolio that
is invested in an S&P index fund
and invested in a Core bond fund. Let x represent
the S&P 500 and y represent the Core Bond fund. Round
your answers to one decimal place. In
percentage terms, what is the expected return and standard deviation for such
a portfolio? Round your answers to two decimal places.
d.
Construct a portfolio that
is invested in an S&P index fund
and invested in a Core bond fund. Let x represent
the S&P 500 and y represent the Core Bond fund. Round
your answers to one decimal place. In
percentage terms, what is the expected return and standard deviation for such
a portfolio? Round your answers to two decimal places.
e.
Which of the portfolios in parts (b),
(c), and (d) above has the largest expected return? Which
has the smallest standard deviation? Which
of these portfolios is the best investment alternative? f. Discuss the advantages and
disadvantages of investing in the three portfolios in parts (b), (c),
and (d). If
your goal is to have the largest return, which portfolio should you choose? If
your goal is to have the least risk, which portfolio should you choose?
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Consider
a binomial experiment with and . a. Compute (to 4 decimals). b. Compute (to 4 decimals). c. Compute (to 4 decimals). d. Compute (to 4 decimals). e. Compute . f. Compute (to 1 decimal)
and (to 2 decimals).
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The
Center for Medicare and Medical Services reported that there
were appeals for hospitalization and other Part A Medicare
service. For this group, of first round appeals were successful (The
Wall Street Journal). Suppose first-round appeals have just
been received by a Medicare appeals office. Refer to Binomial Probability Table. Round
your answers to four decimal places. a. Compute the probability that none
of the appeals will be successful. b. Compute the probability that
exactly one of the appeals will be successful. c. What is the probability that at
least two of the appeals will be successful? d. What is the probability that more
than half of the appeals will be successful?
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Market-share-analysis
company Net Applications monitors and reports on Internet browser usage.
According to Net Applications, in the summer of , Google's Chrome
browser exceeded a market share for the first time, with
a share of the browser market (Forbes website). For a
randomly selected group of Internet browser users, answer the
following questions. a.
Compute the probability that
exactly of the Internet browser users use Chrome as
their Internet browser (to 4 decimals). For this question, if you compute the
probability manually, make sure to carry at least six decimal digits in your
calculations. b.
Compute the probability that at
least of the Internet browser users use Chrome as their
Internet browser (to 4 decimals). c.
For the sample
of Internet browser users, compute the expected number of Chrome
users (to 3 decimals). d.
For the sample
of Internet browser users, compute the variance and standard
deviation for the number of Chrome users (to 3 decimals).
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A
university found that of its students withdraw without completing
the introductory statistics course. Assume that students
registered for the course. a. Compute the probability
that or fewer will withdraw (to 4 decimals). b. Compute the probability that
exactly will withdraw (to 4 decimals). c. Compute the probability that
more than will withdraw (to 4 decimals). d. Compute the expected number
of withdrawals.
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According
to a Wired magazine article, of e-mails
that are received are tracked using software that can tell the e-mail sender
when, where, and on what type of device the e-mail was opened (Wired magazine
website). Suppose we randomly select received e-mails. a.
What is the expected number of
these e-mails that are tracked? b.
What are the variance (to the
nearest whole number) and standard deviation (to 3 decimals) for the number
of these e-mails that are tracked?
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Emergency calls
to a small municipality in Idaho come in at the rate of one
every minutes. a.
What is the expected number
of calls in one hour? b.
What is the probability of
three calls in five minutes (to 4 decimals)? c.
What is the probability of
no calls in a five-minute period (to 4 decimals)?
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Airline
passengers arrive randomly and independently at the passenger-screening
facility at a major international airport. The mean arrival rate
is passengers per minute. a. Compute the probability of no
arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three
or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no
arrivals in a -second period (to 4 decimals). d. Compute the probability of at least
one arrival in a -second period (to 4 decimals).
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According
to a survey conducted by the technology market research firm The
Radicati Group, U.S. office workers receive an average of e-mails
per day (Entrepreneur magazine website). Assume the number of
e-mails received per hour follows a Poisson distribution and that the average
number of e-mails received per hour is five. a.
What is the probability of
receiving no e-mails during an hour (to 4 decimals)? b.
What is the probability of
receiving at least three e-mails during an hour (to 4 decimals)? For this
question, if calculating the probability manually make sure to carry at least
4 decimal digits in your calculations. c.
What is the expected number of
e-mails received during minutes (to 2 decimals)? d.
What is the probability that no
e-mails are received during minutes (to 4 decimals)?
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Suppose and . What
is the probability of for (to 4 decimals)?
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The
Zagat Restaurant Survey provides food, decor, and service ratings for some of
the top restaurants across the United States. For restaurants
located in Boston, the average price of a dinner, including one drink and
tip, was . You are leaving on a business trip to Boston and will eat
dinner at three of these restaurants. Your company will reimburse you for a
maximum of per dinner. Business associates familiar with these
restaurants have told you that the meal cost at one-third of these restaurants
will exceed . Suppose that you randomly select three of these
restaurants for dinner. a.
What is the probability that none
of the meals will exceed the cost covered by your company (to 4 decimals)? b.
What is the probability that one of
the meals will exceed the cost covered by your company (to 4 decimals)? c.
What is the probability that two of
the meals will exceed the cost covered by your company (to 4 decimals)? d.
What is the probability that all
three of the meals will exceed the cost covered by your company (to 4
decimals)?
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Delta
Airlines quotes a flight time of hours, minutes for its
flights from Cincinnati to Tampa. Suppose we believe that actual flight times
are uniformly distributed between hours
and hours, minutes. a. Which of the following graphs
accurately represents the probability density function for flight time in
minutes?
b. What is the probability that
the flight will be no more than 5 minutes late (to 2 decimals)? c. What is the probability that
the flight will be more than 10 minutes late (to 2 decimals)? d. What is the expected flight
time, in minutes?
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The
electric-vehicle manufacturing company Tesla estimates that a driver who
commutes miles per day in a Model S will require a nightly charge
time of around hour and minutes ( minutes) to
recharge the vehicle's battery (Tesla company website). Assume that the
actual recharging time required is uniformly distributed between and minutes. a. Give a mathematical expression for
the probability density function of battery recharging time for this
scenario.
The
correct answer is: b. What is the probability that the
recharge time will be less than minutes (to 3 decimals)? c. What is the probability that
the recharge time required is at least minutes (to 3 decimals)? d. What is the probability that the
recharge time required is between and minutes (to 3
decimals)?
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Suppose
we are interested in bidding on a piece of land and we know one other bidder
is interested. The seller announced that the highest bid in excess
of will be accepted. Assume that the competitor's
bid is a random variable that is uniformly distributed
between and . a. Suppose you bid . What
is the probability that your bid will be accepted (to 2 decimals)? b. Suppose you bid . What
is the probability that your bid will be accepted (to 2 decimals)? c. What amount should you bid to
maximize the probability that you get the property? $ d. Suppose that you know someone
is willing to pay you for the property. You are considering
bidding the amount shown in part (c) but a friend suggests you bid .
Which bid will give you the larger expected profit? What
is the expected profit for this bid (to 2 decimals)? $
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A
random variable is normally distributed with a mean of and a
standard deviation of . a. Which of the following graphs
accurately represents the probability density function?
Choose
the correct option. b. What is the probability that
the random variable will assume a value between and (to
4 decimals)? c. What is the probability that
the random variable will assume a value between and (to
4 decimals)?
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Given
that is a standard normal random variable, compute the following
probabilities (to 4 decimals). a. b. c. d. e.
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Males
in the Netherlands are the tallest, on average, in the world with an average
height of centimeters (cm) (BBC News website). Assume that the
height of men in the Netherlands is normally distributed with a mean
of cm and standard deviation of cm. a.
What is the probability that a
Dutch male is shorter than cm (to 4 decimals)? b.
What is the probability that a
Dutch male is taller than cm (to 4 decimals)? c.
What is the probability that a
Dutch male is between and cm (to 4 decimals)? d.
Out of a random sample
of Dutch men, how many would we expect to be taller
than cm (rounded to the nearest whole number)?
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A
person must score in the upper of the population on an IQ test to
qualify for membership in Mensa, the international high-IQ society. If IQ
scores are normally distributed with a mean of and a standard
deviation of , what score must a person have to qualify for Mensa (to
whole number)?
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The
time needed to complete a final examination in a particular college course is
normally distributed with a mean of minutes and a standard
deviation of minutes. Answer the following questions. a. What is the probability of
completing the exam in one hour or less (to 4 decimals)?
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According
to Money magazine, Maryland had the highest median annual
household income of any state in at (Time.com website).
Assume that annual household income in Maryland follows a normal distribution
with a median of and standard deviation of . a.
What is the probability that a
household in Maryland has an annual income of or more (to 4
decimals)? b.
What is the probability that a
household in Maryland has an annual income of or less (to 4
decimals)? c.
What is the probability that a
household in Maryland has an annual income
between and (to 4 decimals)? d.
What is the annual income of a
household in the percentile of annual household income in Maryland
(to the nearest dollar)?
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Alexa
is the popular virtual assistant developed by Amazon. Alexa interacts with
users using artificial intelligence and voice recognition. It can be used to
perform daily tasks such as making to-do lists, reporting the news and
weather, and interacting with other smart devices in the home. In , the
Amazon Alexa app was downloaded some times per day from the Google
Play store (AppBrain website). Assume that the number of downloads per day of
the Amazon Alexa app is normally distributed with a mean of and standard
deviation of . a.
What is the probability there
are or fewer downloads of Amazon Alexa in a day (to 4 decimals)? b.
What is the probability there are
between and downloads of Amazon Alexa in a day (to 4
decimals)? c.
What is the probability there are
more than downloads of Amazon Alexa in a day (to 4 decimals)? d.
Assume that Google has designed its
servers so there is probability that the number of Amazon Alexa
app downloads in a day exceeds the servers' capacity and more servers have to
be brought online. How many Amazon Alexa app downloads per day are Google's
servers designed to handle (to the nearest whole number)? downloads
per day
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The
XO Group Inc. conducted a survey of brides and grooms
married in the United States and found that the average cost of a wedding
is (XO Group website). Assume that the cost of a wedding is
normally distributed with a mean of and a standard deviation
of . a.
What is the probability that a
wedding costs less than (to 4 decimals)? b.
What is the probability that a
wedding costs between and (to 4 decimals)? c.
For a wedding to be among
the most expensive, how much would it have to cost (to the nearest
whole number)?
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According
to the National Association of Colleges and Employers, the average
starting salary for new college graduates in health sciences was . The
average starting salary for new college graduates in business
was (National Association of Colleges and Employers website).
Assume that starting salaries are normally distributed and that the standard
deviation for starting salaries for new college graduates in health sciences
is . Assume that the standard deviation for starting salaries for new
college graduates in business is . a.
What is the probability that a new
college graduate in business will earn a starting salary of at
least (to 4 decimals)? b.
What is the probability that a new
college graduate in health sciences will earn a starting salary of at
least (to 4 decimals)? c.
What is the probability that a new
college graduate in health sciences will earn a starting salary less
than (to 4 decimals)? d.
How much would a new college
graduate in business have to earn in order to have a starting salary higher
than of all starting salaries of new college graduates in the
health sciences (to the nearest whole number)?
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Do
you dislike waiting in line? Supermarket chain Kroger has used computer
simulation and information technology to reduce the average waiting time for
customers at stores. Using a new system called QueVision,
which allows Kroger to better predict when shoppers will be checking out, the
company was able to decrease average customer waiting time to
just seconds (InformationWeek website). Assume that
waiting times at Kroger are exponentially distributed. a.
Which of the probability density
functions of waiting time is applicable at Kroger? a. for b. for c. for d. for b.
What is the probability that a
customer will have to wait between and seconds (to 4
decimals)? c.
What is the probability that a
customer will have to wait more than minutes (to 4 decimals)?
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Consider
the following exponential probability density function. for a. Which of the following is the
formula for ?
b. Find (to 4 decimals). c. Find (to 4 decimals). d. Find (to 4 decimals). e. Find (to 4 decimals).
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Intensive
care units (ICUs) generally treat the sickest patients in a hospital. ICUs
are often the most expensive department in a hospital because of the
specialized equipment and extensive training required to be an ICU doctor or
nurse. Therefore, it is important to use ICUs as efficiently as possible in a
hospital. According to a large-scale study of elderly ICU
patients, the average length of stay in the ICU is days (Critical
Care Medicine journal article). Assume that this length of stay in
the ICU has an exponential distribution. Do not round intermediate
calculations. a.
What is the probability that the
length of stay in the ICU is one day or less (to 4 decimals)? b.
What is the probability that the
length of stay in the ICU is between two and three days (to 4 decimals)? c.
What is the probability that the
length of stay in the ICU is more than five days (to 4 decimals)?
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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.
Refer to Exhibit 6-6. What percentage of tires will have a life of 34,000 to 46,000 miles?
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The probability that x will take on a value of at least 26 is _____.
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