Discrete Probability Distributions 5-1
CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS
1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio–
Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that
the teacher on bus duty will likely be certified in CPR?
a) 5 days
b) 45 days
c) 65 days
d) 81 days
2. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4
students is selected from the program to be interviewed about the introduction of a new fast food
outlet on the ground floor of the campus building, what is the probability that all 4 students
selected are undergraduate students?
a) 0.0256
b) 0.0625
c) 0.16
d) 1.00
3. A probability distribution is an equation that
a) associates a particular probability of occurrence with each outcome.
b) measures outcomes and assigns values of X to the simple events.
c) assigns a value to the variability of the set of events.
d) assigns a value to the center of the set of events.
4. The connotation “expected value” or “expected gain” from playing roulette at a casino means
a) the amount you expect to “gain” on a single play.
b) the amount you expect to “gain” in the long run over many plays.
c) the amount you need to “break even” over many plays.
d) the amount you should expect to gain if you are lucky.
5-2 Discrete Probability Distributions
5. Which of the following about the binomial distribution is not a true statement?
a) The probability of the event of interest must be constant from trial to trial.
b) Each outcome is independent of the other.
c) Each outcome may be classified as either “event of interest” or “not event of interest.”
d) The variable of interest is continuous.
6. In a binomial distribution
a) the variable X is continuous.
b) the probability of event of interest
is stable from trial to trial.
c) the number of trials n must be at least 30.
d) the results of one trial are dependent on the results of the other trials.
7. Whenever
= 0.5, the binomial distribution will
a) always be symmetric.
b) be symmetric only if n is large.
c) be right-skewed.
d) be left-skewed.
8. Whenever
= 0.1 and n is small, the binomial distribution will be
a) symmetric.
b) right-skewed.
c) left-skewed.
d) None of the above.
Discrete Probability Distributions 5-3
9. If n = 10 and
= 0.70, then the mean of the binomial distribution is
a) 0.07
b) 1.45.
c) 7.00
d) 14.29
10. If n = 10 and
= 0.70, then the standard deviation of the binomial distribution is
a) 0.07
b) 1.45
c) 7.00
d) 14.29
11. If the outcomes of a variable follow a Poisson distribution, then their
a) mean equals the standard deviation.
b) median equals the standard deviation.
c) mean equals the variance.
d) median equals the variance.
12. What type of probability distribution will the consulting firm most likely employ to analyze the
insurance claims in the following problem?
An insurance company has called a consulting firm to determine if the company has an
unusually high number of false insurance claims. It is known that the industry proportion for
false claims is 3%. The consulting firm has decided to randomly and independently sample
100 of the company’s insurance claims. They believe the number of these 100 that are false
will yield the information the company desires.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
5-4 Discrete Probability Distributions
13. The covariance
a) must be between -1 and +1.
b) must be positive.
c) can be positive or negative.
d) must be less than +1.
14. What type of probability distribution will most likely be used to analyze warranty repair needs on
new cars in the following problem?
The service manager for a new automobile dealership reviewed dealership records of the past
20 sales of new cars to determine the number of warranty repairs he will be called on to
perform in the next 90 days. Corporate reports indicate that the probability any one of their
new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls
for warranty repair are independent of one another and is interested in predicting the number
of warranty repairs he will be called on to perform in the next 90 days for this batch of 20
new cars sold.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
15. What type of probability distribution will most likely be used to analyze the number of blue
chocolate chips per bag in the following problem?
The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.
When the production process is in control, the mean number of blue chocolate chips per bag
is 6.0. The manager is interested in analyzing the probability that any particular bag being
inspected has fewer than 5.0 blue chocolate chips.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
Discrete Probability Distributions 5-5
16. What type of probability distribution will most likely be used to analyze the number of cars with
defective radios in the following problem?
From an inventory of 48 new cars being shipped to local dealerships, corporate reports
indicate that 12 have defective radios installed. The sales manager of one dealership wants to
predict the probability out of the 8 new cars it just received that, when each is tested, no
more than 2 of the cars have defective radios.
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
17. A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the
list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of
only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from
the list, he would use what type of probability distribution to compute the probability that all of
the chosen stocks would appreciate more than 20% after 30 days?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
18. A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.
To compute the probability of receiving at least 10 e-mails on such a day, he will use what type
of probability distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
5-6 Discrete Probability Distributions
19. A company has 125 personal computers. The probability that any one of them will require repair
on a given day is 0.025. To find the probability that exactly 20 of the computers will require
repair on a given day, one will use what type of probability distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
20. The portfolio expected return of two investments
a) will be higher when the covariance is zero.
b) will be higher when the covariance is negative.
c) will be higher when the covariance is positive.
d) does not depend on the covariance.
21. A financial analyst is presented with information on the past records of 60 start-up companies
and told that in fact only 3 of them have managed to become highly successful. He selected 3
companies from this group as the candidates for success. To analyze his ability to spot the
companies that will eventually become highly successful, he will use what type of probability
distribution?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
Discrete Probability Distributions 5-7
22. On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery
store. What type of probability distribution can be used to find out the probability that there will
be no customer arriving at a checkout counter?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
23. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who
has not studied for the test decides to answer all questions randomly. What type of probability
distribution can be used to figure out his chance of getting at least 20 questions right?
a) binomial distribution.
b) Poisson distribution.
c) hypergeometric distribution.
d) none of the above.
24. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab
conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per
week. Interpret this value.
a) Most of the weeks resulted in rat costs of $13.00.
b) The median cost for the distribution of rat costs is $13.00.
c) The expected or mean cost for all weekly rat purchases is $13.00.
d) The rat cost that occurs more often than any other is $13.00.
5-8 Discrete Probability Distributions
25. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab
conducts. Prices for 100 rats follow the following distribution:
Price: $10.00 $12.50 $15.00
Probability: 0.35 0.40 0.25
How much should the lab budget for next year’s rat orders be, assuming this distribution does not
change?
a) $520
b) $637
c) $650
d) $780
26. The local police department must write, on average, 5 tickets a day to keep department revenues
at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution
with a mean of 6.5 tickets per day. Interpret the value of the mean.
a) The number of tickets that is written most often is 6.5 tickets per day.
b) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5
tickets written.
c) If we sampled all days, the arithmetic average or expected number of tickets written
would be 6.5 tickets per day.
d) The mean has no interpretation since 0.5 ticket can never be written.
27. True or False: The Poisson distribution can be used to model a continuous random variable.
28. True or False: Another name for the mean of a probability distribution is its expected value.
Discrete Probability Distributions 5-9
29. True or False: The number of customers arriving at a department store in a 5-minute period has a
binomial distribution.
30. True or False: The number of customers arriving at a department store in a 5-minute period has a
Poisson distribution.
31. True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a binomial distribution.
32. True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a hypergeometric distribution.
33. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.
34. True or False: The largest value that a Poisson random variable X can have is n.
5-10 Discrete Probability Distributions
35. True or False: In a Poisson distribution, the mean and standard deviation are equal.
36. True or False: In a Poisson distribution, the mean and variance are equal.
37. True or False: If
remains constant in a binomial distribution, an increase in n will increase the
variance.
38. True or False: If
remains constant in a binomial distribution, an increase in n will not change
the mean.
39. True or False: Suppose that a judge’s decisions follow a binomial distribution and that his verdict
is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2
incorrect verdicts is 0.736.
40. True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson
process. The mean number of airplanes arriving per minute is 3. The probability that exactly 6
planes arrive in the next minute is 0.05041.
Discrete Probability Distributions 5-11
41. True or False: The covariance between two investments is equal to the sum of the variances of
the investments.
42. True or False: If the covariance between two investments is zero, the variance of the sum of the
two investments will be equal to the sum of the variances of the investments.
43. True or False: The expected return of the sum of two investments will be equal to the sum of the
expected returns of the two investments plus twice the covariance between the investments.
44. True or False: The variance of the sum of two investments will be equal to the sum of the
variances of the two investments plus twice the covariance between the investments.
45. True or False: The variance of the sum of two investments will be equal to the sum of the
variances of the two investments when the covariance between the investments is zero.
46. True or False: The expected return of a two-asset portfolio is equal to the product of the weight
assigned to the first asset and the expected return of the first asset plus the product of the weight
assigned to the second asset and the expected return of the second asset.
5-12 Discrete Probability Distributions
SCENARIO 5-1
The probability that a particular type of smoke alarm will function properly and sound an alarm in
the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.
47. Referring to Scenario 5-1, the probability that both sound an alarm in the presence of smoke is
________.
48. Referring to Scenario 5-1, the probability that neither sound an alarm in the presence of smoke is
________.
49. Referring to Scenario 5-1, the probability that at least one sounds an alarm in the presence of
smoke is ________.
SCENARIO 5-2
A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open
(where they do not compete with each other, so it is reasonable to believe that their relative successes
would be independent).
50. Referring to Scenario 5-2, the probability that all 3 businesses succeed is ________.
51. Referring to Scenario 5-2, the probability that all 3 businesses fail is ________.
Discrete Probability Distributions 5-13
52. Referring to Scenario 5-2, the probability that at least 1 business succeeds is ________.
53. Referring to Scenario 5-2, the probability that exactly 1 business succeeds is ________.
54. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .
55. If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .
56. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .
57. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 1 prefers brand C is ________.
58. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that at least 1 prefers brand C is ________.
5-14 Discrete Probability Distributions
59. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 3 prefer brand C is ________.
60. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 4 prefer brand C is ________.
61. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that 2 or fewer prefer brand C is ________.
62. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that more than 3 prefer brand C is ________.
63. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that fewer than 2 prefer brand C is ________.
64. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The mean number that you would expect to prefer brand C is
________.
Discrete Probability Distributions 5-15
65. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The variance of the number that prefer brand C is ________.
SCENARIO 5-3
The following table contains the probability distribution for X = the number of retransmissions
necessary to successfully transmit a 1024K data package through a network.
X
0
1
2
3
P(X)
0.35
0.35
0.25
0.05
66. Referring to Scenario 5-3, the probability of no retransmissions is ________.
67. Referring to Scenario 5-3, the probability of at least one retransmission is ________.
68. Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is
________.
69. Referring to Scenario 5-3, the variance for the number of retransmissions is ________.
70. Referring to Scenario 5-3, the standard deviation of the number of retransmissions is ________.
5-16 Discrete Probability Distributions
71. In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she does not get audited is ________.
72. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited once is ________.
73. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited at least once is ________.
74. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited no more than 2 times is ________.
75. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The expected number of times she will be audited is ________.
Discrete Probability Distributions 5-17
76. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The variance of the number of times she will be audited is ________.
77. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The standard deviation of the number of times she will be audited is ________.
SCENARIO 5-4
The following table contains the probability distribution for X = the number of traffic accidents
reported in a day in a small city in the Midwest.
0
1
2
3
4
5
0.10
0.20
0.45
0.15
0.05
0.05
78. Referring to Scenario 5-4, the probability of 3 accidents is ________.
79. Referring to Scenario 5-4, the probability of at least 1 accident is ________.
80. Referring to Scenario 5-4, the mean or expected value of the number of accidents is ________.
5-18 Discrete Probability Distributions
81. Referring to Scenario 5-4, the variance of the number of accidents is ________.
82. Referring to Scenario 5-4, the standard deviation of the number of accidents is ________.
83. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The probability that there will be exactly 3 power outages in a year is
____________.
84. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The probability that there will be at least 3 power outages in a year is
____________.
85. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The probability that there will be at least 1 power outage in a year is
____________.
86. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The probability that there will be no more than 1 power outage in a year is
____________.
Discrete Probability Distributions 5-19
87. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The probability that there will be between 1 and 3 inclusive power outages in
a year is ____________.
88. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of
6 outages per year. The variance of the number of power outages is ____________.
89. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.
The probability of seven 911 calls in a day is ____________.
90. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.
The probability of seven or eight 911 calls in a day is ____________.
91. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.
The probability of 2 or more 911 calls in a day is ____________.
92. The number of 911 calls in a small city has a Poisson distribution with a mean of 10.0 calls a
day. The standard deviation of the number of 911 calls in a day is ____________.
5-20 Discrete Probability Distributions
93. An Undergraduate Study Committee of 6 members at a major university is to be formed from a
pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is
the probability that precisely half of the members will be women?
94. An Undergraduate Study Committee of 6 members at a major university is to be formed from a
pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is
the probability that all of the members will be men?
95. A debate team of 4 members for a high school will be chosen randomly from a potential group of
15 students. Ten of the 15 students have no prior competition experience while the others have
some degree of experience. What is the probability that none of the members chosen for the
team have any competition experience?
96. A debate team of 4 members for a high school will be chosen randomly from a potential group of
15 students. Ten of the 15 students have no prior competition experience while the others have
some degree of experience. What is the probability that at least 1 of the members chosen for the
team have some prior competition experience?
97. A debate team of 4 members for a high school will be chosen randomly from a potential group of
15 students. Ten of the 15 students have no prior competition experience while the others have
some degree of experience. What is the probability that no more than 1 of the members chosen
for the team have some prior competition experience?
Discrete Probability Distributions 5-21
98. A debate team of 4 members for a high school will be chosen randomly from a potential group of
15 students. Ten of the 15 students have no prior competition experience while the others have
some degree of experience. What is the probability that exactly half of the members chosen for
the team have some prior competition experience?
99. The Department of Commerce in a particular state has determined that the number of small
businesses that declare bankruptcy per month is approximately a Poisson distribution with a
mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.
100. The Department of Commerce in a particular state has determined that the number of small
businesses that declare bankruptcy per month is approximately a Poisson distribution with a
mean of 6.4. Find the probability that exactly 5 bankruptcies occur next month.
101. Current estimates suggest that 75% of the home-based computers in a foreign country have
access to on-line services. Suppose 20 people with home-based computers were randomly and
independently sampled. Find the probability that fewer than 10 of those sampled currently have
access to on-line services.
102. Current estimates suggest that 75% of the home-based computers in a foreign country have
access to on-line services. Suppose 20 people with home-based computers were randomly and
independently sampled. Find the probability that more than 9 of those sampled currently do not
have access to on-line services.
5-22 Discrete Probability Distributions
103. A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that
women particularly like. A recent survey of American hotels found that 70% offer hairdryers in
the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all
of the hotels in the sample offered hairdryers in the bathrooms.
104. A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that
women particularly like. A recent survey of American hotels found that 70% offer hairdryers in
the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that
more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.
105. A national trend predicts that women will account for half of all business travelers in the next 3
years. To attract these women business travelers, hotels are providing more amenities that
women particularly like. A recent survey of American hotels found that 70% offer hairdryers in
the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that
at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.
106. The local police department must write, on average, 5 tickets a day to keep department
revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson
distribution with a mean of 6.4 tickets per day. Find the probability that less than 6 tickets are
written on a randomly selected day from this population.
Discrete Probability Distributions 5-23
107. The local police department must write, on average, 5 tickets a day to keep department
revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson
distribution with a mean of 6.4 tickets per day. Find the probability that exactly 6 tickets are
written on a randomly selected day from this population.
SCENARIO 5-5
From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that
12 have defective radios installed.
108. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, no more than 2 of the cars have defective radios?
109. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, exactly half of the cars have defective radios?
110. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, none of the cars have defective radios?
111. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, at least half of the cars have defective radios?
5-24 Discrete Probability Distributions
112. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, no more than half of the cars have defective radios?
113. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, no more than 2 of the cars have defective radios?
114. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, exactly two of the cars have non-defective radios?
115. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, at most three of the cars have non-defective radios?
116. Referring to Scenario 5-5, what is the probability out of the 8 new cars it just received that,
when each is tested, no more than half of the cars have non-defective radios?
Discrete Probability Distributions 5-25
SCENARIO 5-6
The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact
fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per
shift is 6.0.
117. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced 4.0 bad bulbs.
118. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced fewer than 5.0 bad bulbs.
119. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced at least 6.0 bad bulbs.
120. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced between 5.0 and 8.0 inclusive bad bulbs.
121. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
less than 5.0 or more than 8.0 bad bulbs.
5-26 Discrete Probability Distributions
SCENARIO 5-7
There are two houses with almost identical characteristics available for investment in two different
neighborhoods with drastically different demographic composition. The anticipated gain in value
when the houses are sold in 10 years has the following probability distribution:
Returns
Probability
Neighborhood A
Neighborhood B
.25
$22,500
$30,500
.40
$10,000
$25,000
.35
$40,500
$10,500
122. Referring to Scenario 5-7, what is the expected value gain for the house in neighborhood A?
123. Referring to Scenario 5-7, what is the expected value gain for the house in neighborhood B?
124. Referring to Scenario 5-7, what is the variance of the gain in value for the house in
neighborhood A?
125. Referring to Scenario 5-7, what is the variance of the gain in value for the house in
neighborhood B?
126. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in
neighborhood A?
Discrete Probability Distributions 5-27
127. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in
neighborhood B?
128. Referring to Scenario 5-7, what is the covariance of the two houses?
129. Referring to Scenario 5-7, what is the expected value gain if you invest in both houses?
130. Referring to Scenario 5-7, what is the total variance of value gain if you invest in both houses?
131. Referring to Scenario 5-7, what is the total standard deviation of value gain if you invest in
both houses?
132. Referring to Scenario 5-7, if you can invest half of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?
5-28 Discrete Probability Distributions
133. Referring to Scenario 5-7, if you can invest half of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?
134. Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?
135. Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?
136. Referring to Scenario 5-7, if you can invest 30% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?
137. Referring to Scenario 5-7, if you can invest 30% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?
Discrete Probability Distributions 5-29
138. Referring to Scenario 5-7, if you can invest 70% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?
139. Referring to Scenario 5-7, if you can invest 70% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?
140. Referring to Scenario 5-7, if you can invest 90% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio expected return of
your investment?
141. Referring to Scenario 5-7, if you can invest 90% of your money on the house in neighborhood
A and the remaining on the house in neighborhood B, what is the portfolio risk of your
investment?
142. Referring to Scenario 5-7, if your investment preference is to maximize your expected return
while exposing yourself to the minimal amount of risk, will you choose a portfolio that will
consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the
remaining on the house in neighborhood B?
5-30 Discrete Probability Distributions
143. Referring to Scenario 5-7, if your investment preference is to maximize your expected return
and not worry at all about the risk that you have to take, will you choose a portfolio that will
consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the
remaining on the house in neighborhood B?
144. Referring to Scenario 5-7, if your investment preference is to minimize the amount of risk that
you have to take and do not care at all about the expected return, will you choose a portfolio that
will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A
and the remaining on the house in neighborhood B?
SCENARIO 5-8
Two different designs on a new line of winter jackets for the coming winter are available for your
manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers
when winter arrives. The probability of the three possible different tastes of the consumers and the
corresponding profits are presented in the following table.
Probability
Taste
Design A
Design B
0.2
more conservative
180
520
0.5
no change
230
310
0.3
more liberal
350
270
145. Referring to Scenario 5-8, the table above is called the ______________ for the two designs.
146. Referring to Scenario 5-8, what is your expected profit when Design A is chosen?
Discrete Probability Distributions 5-31
147. Referring to Scenario 5-8, what is your expected profit when Design B is chosen?
148. Referring to Scenario 5-8, what is the variance of your profit when Design A is chosen?
149. Referring to Scenario 5-8, what is the variance of your profit when Design B is chosen?
150. Referring to Scenario 5-8, what is the standard deviation of your profit when Design A is
chosen?
151. Referring to Scenario 5-8, what is the standard deviation of your profit when Design B is
chosen?
152. Referring to Scenario 5-8, what is the covariance of the profits from the two different designs?
5-32 Discrete Probability Distributions
153. Referring to Scenario 5-8, what is the expected profit if you increase the shift of your
production lines and choose to produce both designs?
154. Referring to Scenario 5-8, what is the total variance of the profit if you increase the shift of
your production lines and choose to produce both designs?
155. Referring to Scenario 5-8, what is the total standard deviation of the profit if you increase the
shift of your production lines and choose to produce both designs?
156. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and
Design B for the other half, what is your expected profit?
157. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and
Design B for the other half, what is the risk of your investment?
158. Referring to Scenario 5-8, if you decide to choose Design A for half of the production lines and
Design B for the other half, what is the coefficient of variation of your investment?
Discrete Probability Distributions 5-33
159. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines
and Design B for the remaining production lines, what is the expected profit?
160. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines
and Design B for the remaining production lines, what is the risk of your investment?
161. Referring to Scenario 5-8, if you decide to choose Design A for 10% of the production lines
and Design B for the remaining production lines, what is the coefficient of variation of your
investment?
162. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines
and Design B for the remaining production lines, what is the expected profit?
163. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines
and Design B for the remaining production lines, what is the risk of your investment?
164. Referring to Scenario 5-8, if you decide to choose Design A for 30% of the production lines
and Design B for the remaining production lines, what is the coefficient of variation of your
investment?
5-34 Discrete Probability Distributions
165. Referring to Scenario 5-8, if you decide to choose Design A for 70% of the production lines
and Design B for the remaining production lines, what is the expected profit?
166. Referring to Scenario 5-8 if you decide to choose Design A for 70% of the production lines and
Design B for the remaining production lines, what is the risk of your investment?
167. Referring to Scenario 5-8, if you decide to choose Design A for 70% of the production lines
and Design B for the remaining production lines, what is the coefficient of variation of your
investment?
168. Referring to Scenario 5-8, if you decide to choose Design A for 90% of the production lines
and Design B for the remaining production lines, what is the expected profit?
169. Referring to Scenario 5-8 if you decide to choose Design A for 90% of the production lines and
Design B for the remaining production lines, what is the risk of your investment?
170. Referring to Scenario 5-8, if you decide to choose Design A for 90% of the production lines
and Design B for the remaining production lines, what is the coefficient of variation of your
investment?
Discrete Probability Distributions 5-35
171. Referring to Scenario 5-8, if your investment preference is to maximize your expected profit
while exposing yourself to the minimal amount of risk, will you choose a production mix that
will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the
remaining for Design B?
172. Referring to Scenario 5-8, if your investment preference is to maximize your expected profit
and not worry at all about the risk that you have to take, will you choose a production mix that
will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and the
remaining for Design B?
173. Referring to Scenario 5-8, if your investment preference is to minimize the amount of risk that
you have to take and do not care at all about the expected profit, will you choose a production
mix that will consist of 10%, 30%, 50%, 70%, or 90% of your production lines for Design A and
the remaining for Design B?
SCENARIO 5-9
A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a
recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number
of mishandled bags has a Poisson distribution.
174. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have no mishandled bags?
5-36 Discrete Probability Distributions
175. Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will
have at least one mishandled bags?
176. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have at least two mishandled bags?
177. Referring to Scenario 5-9, what is the probability that in the next 1,000 customer, the hotel
chain will have no more than three mishandled bags?
178. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have no more than four mishandled bags?
179. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have fewer than six mishandled bags?
180. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have fewer than eight mishandled bags?
Discrete Probability Distributions 5-37
181. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have more than eight mishandled bags?
182. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have more than ten mishandled bags?
183. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have between two and four inclusive mishandled bags?
184. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have more than five but less than eight mishandled bags?
185. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have less than two or more than eight mishandled bags?
186. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have no more than two or at least eight mishandled bags?
5-38 Discrete Probability Distributions
187. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have less than two and more than eight mishandled bags?
188. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel
chain will have no more than two and at least eight mishandled bags?
SCENARIO 5-10
An accounting firm in a college town usually recruits employees from two of the universities in
town. This year, there are fifteen graduates from University A and five from University B and the
firm decides to hire six new employees from the two universities.
189. Referring to Scenario 5-10, what is the probability that two of the new employees will be from
University A?
190. Referring to Scenario 5-10, what is the probability that all six of the new employees will be
from University A?
191. Referring to Scenario 5-10, what is the probability that none of the new employees will be
from University B?
Discrete Probability Distributions 5-39
192. Referring to Scenario 5-10, what is the probability that none of the new employees will be
from University A?
193. Referring to Scenario 5-10, what is the probability that all of the new employees will be from
University B?
194. Referring to Scenario 5-10, what is the probability that at least one of the new employees will
be from University A?
195. Referring to Scenario 5-10, what is the probability that no more than four of the new
employees will be from University A?
196. Referring to Scenario 5-10, what is the probability that at least two of the new employees will
be from University B?
197. Referring to Scenario 5-10, what is the probability that more than four of the new employees
will be from University A?
5-40 Discrete Probability Distributions
198. Referring to Scenario 5-10, what is the probability that no more than two of the new employees
will be from University B?
SCENARIO 5-11
Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades
per month. Assume that one of the subscribers performs transactions at this rate and the probability
of a transaction for any two months is the same and the number of transactions in one month is
independent of the number of transactions in another month.
199. Referring to Scenario 5-11, what is mean number of transactions per month for this subscriber?
200. Referring to Scenario 5-11, what is variance of the number of transactions per month for this
subscriber?
201. Referring to Scenario 5-11, what is probability that exactly ten security transactions will be
conducted in one month?
202. Referring to Scenario 5-11, what is probability that at least five security transactions will be
conducted in one month?
Discrete Probability Distributions 5-41
203. Referring to Scenario 5-11, what is probability that no more than five security transactions will
be conducted in one month?
204. Referring to Scenario 5-11, what is probability that no security transaction will be conducted in
one month?
205. Referring to Scenario 5-11, what is probability that more than two security transactions will be
conducted in one month?
206. Referring to Scenario 5-11, what is probability that fewer than two security transactions will be
conducted in one month?