GBS 541
Homework #2
7/4/2019
Due: 15/4/2019
Use formulas, calculations and tables, unless stated otherwise. (Show the formulas
and how you arrive at your solution) You can use MegaStat/Excel to check you
answers
Question 1
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night
in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room
rates for 20 cities are as follows:
Atlanta
Boston
Chicago
Cleveland
Dallas
Denver
Detroit
Houston
Los Angeles
Miami
$163
177
166
126
123
120
144
173
160
192
Minneapolis
New Orleans
New York
Orlando
Phoenix
Pittsburgh
San Francisco
Seattle
St. Louis
Washington, D.C.
$125
167
245
146
139
134
167
162
145
207
a. What is the mean hotel room rate?
b. What is the median hotel room rate?
c. What is the mode?
d. What is the first quartile?
e. What is the third quartile?
Question 2
Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
8408
608
10498
3653
a.
b.
c.
d.
1374
14138
7478
5794
1872
6452
4019
8305
8879
1850
4341
2459
2818
739
11413
1356
2127
Provide a five-number summary.
Compute the lower and upper limits.
Do the data contain any outliers?
Johnson & Johnson’s sales are the largest on the list at $14,138 million. Suppose a
data entry error (a transposition) had been made and the sales had been entered as
$41,138 million. Would the method of detecting outliers in part (c) identify this
problem and allow for correction of the data entry error?
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e. Show a box plot.
Question 3
The Los Angeles Times regularly reports the air quality index for various areas of
Southern California. A sample of air quality index values for Pomona provided the
following data:
28, 42, 58, 48, 45, 55, 60, 49, and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of
48.5, a sample variance of 136, and a sample standard deviation of 11.66. What
comparisons can you make between the air quality in Pomona and that in
Anaheim on the basis of these descriptive statistics?
Question 4
The Energy Information Administration reported that the mean retail price per gallon of
regular grade gasoline was $2.05 (Energy Information Administration, May 2009).
Suppose that the standard deviation was $.10 and that the retail price per gallon has a
bell-shaped distribution.
a. What percentage of regular grade gasoline sold between $1.95 and $2.15 per
gallon?
b. What percentage of regular grade gasoline sold between $1.95 and $2.25 per
gallon?
c. What percentage of regular grade gasoline sold for more than $2.25 per gallon?
Question 5
Consumer Reports posts reviews and ratings of a variety of products on its website. The
following is a sample of 20 speaker systems and their ratings. The ratings are on a scale
of 1 to 5, with 5 being best.
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a.
b.
c.
d.
e.
f.
Compute the mean and the median.
Compute the first and third quartiles.
Compute the standard deviation.
The skewness of this data is -1.67. Comment on the shape of the distribution.
What are the z-scores associated with Allison One and Omni Audio?
Do the data contain any outliers? Explain.
Question 6
Seventy percent of the students applying to a university are accepted. What is the
probability that among the next 18 applicants
a.
b.
c.
d.
e.
f.
At least 6 will be accepted? (Use the binomial probability tables)
Exactly 10 will be accepted? (Use the binomial probability tables)
Exactly 5 will be rejected? (Use the binomial formula)
Fifteen or more will be accepted? (Use the binomial formula)
Determine the expected number of acceptances
Compute the standard deviation.
Question 7
A listing of 46 mutual funds and their 12-month total return percentage is shown in
Table 3.5 (Smart Money, February 2004).
a.
b.
c.
d.
What are the mean and median return percentages for these mutual funds?
What are the first and third quartiles?
Provide a five-number summary.
Do the data contain any outliers? Show a box plot.
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Question 8
At the beginning of 2009, the economic downturn resulted in the loss of jobs and an
increase in delinquent loans for housing. The national unemployment rate was 6.5% and
the percentage of delinquent loans was 6.12% (The Wall Street Journal, January 27,
2009). In projecting where the real estate market was headed in the coming year,
economists studied the relationship between the jobless rate and the percentage of
delinquent loans. The expectation was that if the jobless rate continued to increase, there
would also be an increase in the percentage of delinquent loans. The data below show the
jobless rate and the delinquent loan percentage for 27 major real estate markets.
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a. Compute the correlation coefficient. Is there a positive correlation between the
jobless rate and the percentage of delinquent housing loans? What is your
interpretation?
b. Show a scatter diagram of the relationship between jobless rate and the percentage
of delinquent housing loans.
Question 9
General Hospital has noted that they admit an average of 8 patients per hour.
a. What is the probability that during the next hour less then 3 patients will be admitted?
(Use the poisson probability tables)
b. What is the probability that during the next two hours exactly 8 patients will be
admitted? (Use the poisson formula)
Question 10
The demand for a product varies from month to month. Based on the past year's data, the
following probability distribution shows MNM company's monthly demand.
x
Unit Demand
0
1,000
2,000
3,000
4,000
f(x)
Probability
0.10
0.10
0.30
0.40
0.10
a. Determine the expected number of units demanded per month.
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b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will
the company gain or lose in a month if they stock the expected number of units
demanded, but sell 2000 units?
Question 11
The records show that 8% of the items produced by a machine do not meet the
specifications. Use the normal approximation to the binomial distribution to answer the
following questions. What is the probability that a sample of 100 units contains
a. Five or more defective units?
b. Ten or fewer defective units?
c. Eleven or less defective units?
Question 12
Amayenge Band is giving 14 concerts in November 2017. The shows are all in Africa and
their tour in Africa involves about 40 locations. How many different schedules are
possible? That is, how many different possible combinations of cities are possible when
giving 14 shows from a set of 40 cities?
Question 13
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to
Tampa. Suppose we believe that actual flight times are uniformly distributed between
2 hours and 2 hours, 20 minutes.
a. Show the graph of the probability density function for flight time.
b. What is the probability that the flight will be no more than 5 minutes late?
c. What is the probability that the flight will be more than 10 minutes late?
d. What is the expected flight time?
Question 14
The following frequency distribution shows the price per share of the 30 companies in the
Dow Jones Industrial Average (Barron’s, February 2, 2009).
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a. Compute the mean price per share and the standard deviation of the price per
share for the Dow Jones Industrial Average companies.
b. On January 16, 2006, the mean price per share was $45.83 and the standard
deviation was $18.14. Comment on the changes in the price per share over the
three-year period.
Question 15
In the city of Milford, applications for zoning changes go through a two-step process: a
review by the planning commission and a final decision by the city council. At step 1 the
planning commission reviews the zoning change request and makes a positive or negative
recommendation concerning the change. At step 2 the city council reviews the planning
commission’s recommendation and then votes to approve or to disapprove the zoning
change. Suppose the developer of an apartment complex submits an application for a
zoning change. Consider the application process as an experiment.
a. How many sample points are there for this experiment? List the sample points.
b. Construct a tree diagram for the experiment.
Question 16
In a survey of MBA students, the following data were obtained on “students’ first reason
for application to the school in which they matriculated.”
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a. Develop a joint probability table for these data.
b. Use the marginal probabilities of school quality, school cost or convenience, and
other to comment on the most important reason for choosing a school. c. If a
student goes full time, what is the probability that school quality is the first reason
for choosing a school?
c. If a student goes part time, what is the probability that school quality is the first
reason for choosing a school?
d. Let A denote the event that a student is full time and let B denote the event that the
student lists school quality as the first reason for applying. Are events A and B
independent? Justify your answer.
e. If a student goes full time, what is the probability that school quality is the first
reason for choosing a school?
f. If a student goes part time, what is the probability that school quality is the first
reason for choosing a school?
g. Let A denote the event that a student is full time and let B denote the event that the
student lists school quality as the first reason for applying. Are events A and B
independent? Justify your answer.
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