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
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, mean
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
ANSWER:
b
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: binomial distribution
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.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: probability distribution
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: expected value
5-2 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties
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.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
Discrete Probability Distributions 5-3
Copyright ©2015 Pearson Education, Inc.
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
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, mean
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
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: binomial distribution, standard deviation
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Poisson distribution, mean, standard deviation, properties
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.
ANSWER:
a
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: binomial distribution, properties
5-4 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: covariance, properties
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.
ANSWER:
a
TYPE: MC DIFFICULTY: Difficult
KEYWORDS: binomial distribution, properties
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
Discrete Probability Distributions 5-5
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
5-6 Discrete Probability Distributions
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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.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
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.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: portfolio, mean
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution, properties
Discrete Probability Distributions 5-7
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
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.
ANSWER:
a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mean (expected value), probability distribution
5-8 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: mean (expected value), probability distribution
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.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: mean (expected value), Poisson distribution
27. True or False: The Poisson distribution can be used to model a continuous random variable.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
28. True or False: Another name for the mean of a probability distribution is its expected value.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: mean (expected value)
Discrete Probability Distributions 5-9
Copyright ©2015 Pearson Education, Inc.
29. True or False: The number of customers arriving at a department store in a 5-minute period has a
binomial distribution.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
30. True or False: The number of customers arriving at a department store in a 5-minute period has a
Poisson distribution.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, properties
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.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution, properties
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution, properties
33. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: binomial distribution, properties
34. True or False: The largest value that a Poisson random variable X can have is n.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
5-10 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
35. True or False: In a Poisson distribution, the mean and standard deviation are equal.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
36. True or False: In a Poisson distribution, the mean and variance are equal.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: Poisson distribution, properties
37. True or False: If
remains constant in a binomial distribution, an increase in n will increase the
variance.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
38. True or False: If
remains constant in a binomial distribution, an increase in n will not change
the mean.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, properties
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: binomial distribution, probability
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: Poisson distribution, probability
Discrete Probability Distributions 5-11
Copyright ©2015 Pearson Education, Inc.
41. True or False: The covariance between two investments is equal to the sum of the variances of
the investments.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: covariance, variance
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: covariance, variance
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.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: covariance, variance
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: covariance, variance
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.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: portfolio, mean (expected value)
5-12 Discrete Probability Distributions
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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
________.
ANSWER:
0.64
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
48. Referring to Scenario 5-1, the probability that neither sound an alarm in the presence of smoke is
________.
ANSWER:
0.04
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
49. Referring to Scenario 5-1, the probability that at least one sounds an alarm in the presence of
smoke is ________.
ANSWER:
0.96
TYPE: FI DIFFICULTY: Difficult
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.216
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
51. Referring to Scenario 5-2, the probability that all 3 businesses fail is ________.
ANSWER:
0.064
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
Discrete Probability Distributions 5-13
Copyright ©2015 Pearson Education, Inc.
52. Referring to Scenario 5-2, the probability that at least 1 business succeeds is ________.
ANSWER:
0.936
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
53. Referring to Scenario 5-2, the probability that exactly 1 business succeeds is ________.
ANSWER:
0.288
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
54. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .
ANSWER:
0.4116
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution
55. If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .
ANSWER:
0.3483
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
56. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .
ANSWER:
0.0729
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.0768
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.9898
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
5-14 Discrete Probability Distributions
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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 ________.
ANSWER:
0.3456
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.2592
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.3174
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.3370
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.0870
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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
________.
ANSWER:
3
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution, mean
Discrete Probability Distributions 5-15
Copyright ©2015 Pearson Education, Inc.
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 ________.
ANSWER:
1.2
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution, variance
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 ________.
ANSWER:
0.35
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution
67. Referring to Scenario 5-3, the probability of at least one retransmission is ________.
ANSWER:
0.65
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution
68. Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is
________.
ANSWER:
1.0
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, mean (expected value),
69. Referring to Scenario 5-3, the variance for the number of retransmissions is ________.
ANSWER:
0.80
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, variance
70. Referring to Scenario 5-3, the standard deviation of the number of retransmissions is ________.
ANSWER:
0.894
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, standard deviation
5-16 Discrete Probability Distributions
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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 ________.
ANSWER:
0.2373
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.3955
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.7627
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
0.8965
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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 ________.
ANSWER:
1.25
TYPE: FI DIFFICULTY: Easy
KEYWORDS: binomial distribution, mean (expected value),
Discrete Probability Distributions 5-17
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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 ________.
ANSWER:
0.9375
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution, variance
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 ________.
ANSWER:
0.968
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: binomial distribution, standard deviation
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.
X 0 1 2 3 4 5
P(X) 0.10 0.20 0.45 0.15 0.05 0.05
78. Referring to Scenario 5-4, the probability of 3 accidents is ________.
ANSWER:
0.15
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution
79. Referring to Scenario 5-4, the probability of at least 1 accident is ________.
ANSWER:
0.90
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution
80. Referring to Scenario 5-4, the mean or expected value of the number of accidents is ________.
ANSWER:
2.0
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, mean,
5-18 Discrete Probability Distributions
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81. Referring to Scenario 5-4, the variance of the number of accidents is ________.
ANSWER:
1.4
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, variance
82. Referring to Scenario 5-4, the standard deviation of the number of accidents is ________.
ANSWER:
1.18
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution, standard deviation
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
____________.
ANSWER:
0.0892
TYPE: FI DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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
____________.
ANSWER:
0.9380
TYPE: FI DIFFICULTY: Difficult
KEYWORDS: Poisson distribution
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
____________.
ANSWER:
0.9975
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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
____________.
ANSWER:
0.0174
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
Discrete Probability Distributions 5-19
Copyright ©2015 Pearson Education, Inc.
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 ____________.
ANSWER:
0.1487
TYPE: FI DIFFICULTY: Difficult
KEYWORDS: Poisson distribution
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 ____________.
ANSWER:
6
TYPE: FI DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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 ____________.
ANSWER:
0.0901
TYPE: FI DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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 ____________.
ANSWER:
0.2027
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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 ____________.
ANSWER:
0.9995
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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 ____________.
ANSWER:
3.16
TYPE: FI DIFFICULTY: Easy
KEYWORDS: Poisson distribution
5-20 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0.1213
TYPE: FI DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.1379
TYPE: FI DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.1538
TYPE: FI DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.8462
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.5934
TYPE: FI DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
Discrete Probability Distributions 5-21
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0.3297
TYPE: FI DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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.
ANSWER:
0.8811
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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.
ANSWER:
0.1487
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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.
ANSWER:
0.0039
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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.
ANSWER:
0.0139
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: binomial distribution
5-22 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
0.0008
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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.
ANSWER:
0.2264
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: binomial distribution
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.
ANSWER:
0.1133
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: binomial distribution
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.
ANSWER:
0.3837
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
Discrete Probability Distributions 5-23
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
0.1586
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.6863
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.0773
TYPE: PR DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.0802
TYPE: PR DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.09388
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
5-24 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0.9834
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.6863
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.001543
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.01661
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
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?
ANSWER:
0.09388
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
Discrete Probability Distributions 5-25
Copyright ©2015 Pearson Education, Inc.
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.
ANSWER:
0.1339
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
118. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced fewer than 5.0 bad bulbs.
ANSWER:
0.2851
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
119. Referring to Scenario 5-6, what is the probability that any particular shift being inspected has
produced at least 6.0 bad bulbs.
ANSWER:
0.5543
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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.
ANSWER:
0.5622
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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.
ANSWER:
0.4378
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: Poisson distribution
5-26 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$ 12,550
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, mean (expected value),
123. Referring to Scenario 5-7, what is the expected value gain for the house in neighborhood B?
ANSWER:
$ 21,300
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, mean (expected value),
124. Referring to Scenario 5-7, what is the variance of the gain in value for the house in
neighborhood A?
ANSWER:
583,147,500 dollars2
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, variance
125. Referring to Scenario 5-7, what is the variance of the gain in value for the house in
neighborhood B?
ANSWER:
67,460,000 dollars2
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, variance
126. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in
neighborhood A?
ANSWER:
$24,148.45
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, standard deviation
Discrete Probability Distributions 5-27
Copyright ©2015 Pearson Education, Inc.
127. Referring to Scenario 5-7, what is the standard deviation of the value gain for the house in
neighborhood B?
ANSWER:
$8,213.40
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, standard deviation
128. Referring to Scenario 5-7, what is the covariance of the two houses?
ANSWER:
190,040,000
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, covariance
129. Referring to Scenario 5-7, what is the expected value gain if you invest in both houses?
ANSWER:
$ 33,850
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean of the sum
130. Referring to Scenario 5-7, what is the total variance of value gain if you invest in both houses?
ANSWER:
270,527,500
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, variance of the sum
131. Referring to Scenario 5-7, what is the total standard deviation of value gain if you invest in
both houses?
ANSWER:
$ 16,447.72
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation of the sum
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?
ANSWER:
$ 16,925
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
5-28 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$ 8,223.86
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
$ 20,425
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$ 5,125.12
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
$ 18,675
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$ 2,392.04
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
Discrete Probability Distributions 5-29
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$ 15,175
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$ 14,560.11
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
$ 13,425
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$ 20,947.96
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
30%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value), standard deviation, risk, coefficient of variation
5-30 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
10%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
30%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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.
ANSWER:
probability distribution
TYPE: FI DIFFICULTY: Easy
KEYWORDS: probability distribution
146. Referring to Scenario 5-8, what is your expected profit when Design A is chosen?
ANSWER:
$256 thousands or $256,000
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, mean (expected value)
Discrete Probability Distributions 5-31
Copyright ©2015 Pearson Education, Inc.
147. Referring to Scenario 5-8, what is your expected profit when Design B is chosen?
ANSWER:
$340 thousands or $340,000
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, mean (expected value)
148. Referring to Scenario 5-8, what is the variance of your profit when Design A is chosen?
ANSWER:2
4,144 1, 000
or 4,144,000,000
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, variance
149. Referring to Scenario 5-8, what is the variance of your profit when Design B is chosen?
ANSWER:2
8, 400 1, 000
or 8,400,000,000
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, variance
150. Referring to Scenario 5-8, what is the standard deviation of your profit when Design A is
chosen?
ANSWER:
$64.37391 thousands or $64,373.91
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, standard deviation
151. Referring to Scenario 5-8, what is the standard deviation of your profit when Design B is
chosen?
ANSWER:
$91.65151 thousands or $91,651.51
TYPE: PR DIFFICULTY: Easy
KEYWORDS: portfolio, standard deviation
152. Referring to Scenario 5-8, what is the covariance of the profits from the two different designs?
ANSWER:2
4, 320 1, 000
or 4,320,000,000
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, covariance
5-32 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$596 thousands or $596,000
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean of the sum
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?
ANSWER:2
3, 904 1, 000
or 3,904,000,000
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, variance of the sum
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?
ANSWER:
$62.48200 thousands or $62,482.00
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation of the sum
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?
ANSWER:
$ 298 thousands or $298,000
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$31.241 thousands or $31,241
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
10.48%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, coefficient of variation
Discrete Probability Distributions 5-33
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$ 331.6 thousands or $331,600
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$77.89634 thousands or $77,896.34
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
23.49%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, coefficient of variation
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?
ANSWER:
$314.8 thousands or $314,800
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$51.71615 thousands or $51,716.15
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
16.42%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, coefficient of variation
5-34 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
$281.2 thousands or $281,200
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$31.17948 thousands or $31,179.48
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
11.09%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, coefficient of variation
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?
ANSWER:
$264.4 thousands or $264,400
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
$51.60465 thousands or $ 51,604.65
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
19.52%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, coefficient of variation
Discrete Probability Distributions 5-35
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
50%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value), standard deviation, risk, coefficient of variation
NOTE: 50% yields the lowest coefficient of variation
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?
ANSWER:
10%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, mean (expected value)
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?
ANSWER:
70%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: portfolio, standard deviation, risk
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?
ANSWER:
0.0172
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
5-36 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0.9828
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.9127
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.4218
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.6171
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.7757
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.9452
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
Discrete Probability Distributions 5-37
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0.02320
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.003172
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
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?
ANSWER:
0.5298
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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?
ANSWER:
0.1695
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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?
ANSWER:
0.1105
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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?
ANSWER:
0.2842
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
5-38 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
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?
ANSWER:
0
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: Poisson distribution
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?
ANSWER:
0
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: Poisson distribution
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?
ANSWER:
0.0135 or 1.35%
TYPE: PR DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
190. Referring to Scenario 5-10, what is the probability that all six of the new employees will be
from University A?
ANSWER:
0.1291 or 12.91%
TYPE: PR DIFFICULTY: Easy
KEYWORDS: hypergeometric distribution
191. Referring to Scenario 5-10, what is the probability that none of the new employees will be
from University B?
ANSWER:
0.1291 or 12.91%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
Discrete Probability Distributions 5-39
Copyright ©2015 Pearson Education, Inc.
192. Referring to Scenario 5-10, what is the probability that none of the new employees will be
from University A?
ANSWER:
0 or “it can never happen”
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
193. Referring to Scenario 5-10, what is the probability that all of the new employees will be from
University B?
ANSWER:
0 or “it can never happen”
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
194. Referring to Scenario 5-10, what is the probability that at least one of the new employees will
be from University A?
ANSWER:
1.0 or 100%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
195. Referring to Scenario 5-10, what is the probability that no more than four of the new
employees will be from University A?
ANSWER:
0.4835 or 48.35%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
196. Referring to Scenario 5-10, what is the probability that at least two of the new employees will
be from University B?
ANSWER:
0.4835 or 48.35%
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
197. Referring to Scenario 5-10, what is the probability that more than four of the new employees
will be from University A?
ANSWER:
0.5165 or 51.65%
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: hypergeometric distribution
5-40 Discrete Probability Distributions
Copyright ©2015 Pearson Education, Inc.
198. Referring to Scenario 5-10, what is the probability that no more than two of the new employees
will be from University B?
ANSWER:
0.5165 or 51.65%
TYPE: PR DIFFICULTY: Difficult
KEYWORDS: hypergeometric distribution
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?
ANSWER:
5
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
200. Referring to Scenario 5-11, what is variance of the number of transactions per month for this
subscriber?
ANSWER:
5
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
201. Referring to Scenario 5-11, what is probability that exactly ten security transactions will be
conducted in one month?
ANSWER:
0.0181
TYPE: PR DIFFICULTY: Easy
KEYWORDS: Poisson distribution
202. Referring to Scenario 5-11, what is probability that at least five security transactions will be
conducted in one month?
ANSWER:
0.5595
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
Discrete Probability Distributions 5-41
Copyright ©2015 Pearson Education, Inc.
203. Referring to Scenario 5-11, what is probability that no more than five security transactions will
be conducted in one month?
ANSWER:
0.6160
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
204. Referring to Scenario 5-11, what is probability that no security transaction will be conducted in
one month?
ANSWER:
0.0067
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
205. Referring to Scenario 5-11, what is probability that more than two security transactions will be
conducted in one month?
ANSWER:
0.8753
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
206. Referring to Scenario 5-11, what is probability that fewer than two security transactions will be
conducted in one month?
ANSWER:
0.0404
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: Poisson distribution
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