CHAPTER FIVE
DISCRETE PROBABILITY DISTRIBUTIONS
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, circle the correct answer.
1. The binomial probability distribution is most symmetric when
a. n is 30 or greater
b. n equals p
c. p approaches 1
d. p equals 0.5
2. If one wanted to find the probability of ten customer arrivals in an hour at a service
station, one would generally use the
a. binomial probability distribution
b. Poisson probability distribution
c. hypergeometric probability distribution
d. exponential probability distribution
3. The _____ probability function is based in part on the counting rule for combinations.
a. binomial
b. Poisson
c. hypergeometric
d. exponential
4. To compute the probability that in a random sample of n elements, selected without
replacement, we will obtain x successes, we would use the
a. binomial probability distribution
b. Poisson probability distribution
c. hypergeometric probability distribution
d. exponential probability distribution
5. Experimental outcomes that are based on measurement scales such as time, weight, and
distance can be described by _____ random variables.
a. discrete
b. continuous
c. uniform
d. intermittent
6. Which of the following properties of a binomial experiment is called the stationarity
assumption?
a. The experiment consists of n identical trials.
b. Two outcomes are possible on each trial.
c. The probability of success is the same for each trial.
d. The trials are independent.
7. The function used to compute the probability of x successes in n trials, when the trials are
dependent, is the
a. binomial probability function
b. Poisson probability function
c. hypergeometric probability function
d. exponential probability function
8. The expected value of a random variable is the
a. most probable value
b. simple average of all the possible values
c. median value
d. mean value
9. In a binomial experiment consisting of five trials, the number of different values that x
(the number of successes) can assume is
a. 2
b. 5
c. 6
d. 10
10. A binomial probability distribution with p = .3 is
a. negatively skewed
b. symmetrical
c. positively skewed
d. bimodal
11. A numerical description of the outcome of an experiment is called a
a. descriptive statistic
b. probability function
c. variance
d. random variable
12. A random variable that can assume only a finite number of values is referred to as a(n)
a. infinite sequence
b. finite sequence
c. discrete random variable
d. discrete probability function
13. A continuous random variable may assume
a. any value in an interval or collection of intervals
b. only integer values in an interval or collection of intervals
c. only fractional values in an interval or collection of intervals
d. only the positive integer values in an interval
14. An experiment consists of making 80 telephone calls in order to sell a particular
insurance policy. The random variable in this experiment is the number of sales made.
This random variable is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. None of the answers is correct.
15. The number of customers that enter a store during one day is an example of
a. a continuous random variable
b. a discrete random variable
c. either a continuous or a discrete random variable, depending on the number of
the customers
d. either a continuous or a discrete random variable, depending on the gender of the
customers
16. An experiment consists of measuring the speed of automobiles on a highway by the use
of radar equipment. The random variable in this experiment is speed, measured in miles
per hour. This random variable is a
a. discrete random variable
b. continuous random variable
c. complex random variable
d. None of the answers is correct.
17. The weight of an object, measured in grams, is an example of
a. a continuous random variable
b. a discrete random variable
c. either a continuous or a discrete random variable, depending on the weight of the
object
d. either a continuous or a discrete random variable depending on the units of
measurement
18. The weight of an object, measured to the nearest gram, is an example of
a. a continuous random variable
b. a discrete random variable
c. either a continuous or a discrete random variable, depending on the weight of the
object
d. either a continuous or a discrete random variable depending on the units of
measurement
19. A description of how the probabilities are distributed over the values the random variable
can assume is called a
a. probability distribution
b. probability function
c. random variable
d. expected value
20. Which of the following is(are) required condition(s) for a discrete probability function?
a. f(x) = 0
b. f(x) 1 for all values of x
c. f(x) < 0
d. None of the answers is correct.
21. Which of the following is not a required condition for a discrete probability function?
a. f(x) 0 for all values of x
b. f(x) = 1
c. f(x) = 0
d. All of the answers are correct.
22. Which of the following statements about a discrete random variable and its probability
distribution are true?
a. Values of the random variable can never be negative.
b. Negative values of f(x) are allowed as long as f(x) = 1.
c. Values of f(x) must be greater than or equal to zero.
d. The values of f(x) increase to a maximum point and then decrease.
23. A measure of the average value of a random variable is called a(n)
a. variance
b. standard deviation
c. expected value
d. None of the answers is correct.
24. A weighted average of the value of a random variable, where the probability function
provides weights is known as
a. a probability function
b. a random variable
c. the expected value
d. None of the answers is correct
25. The expected value of a random variable is the
a. value of the random variable that should be observed on the next repeat of the
experiment
b. value of the random variable that occurs most frequently
c. square root of the variance
d. None of the answers is correct.
26. The expected value of a discrete random variable
a. is the most likely or highest probability value for the random variable
b. will always be one of the values x can take on, although it may not be the highest
probability value for the random variable
c. is the average value for the random variable over many repeats of the experiment
d. All of the answers are correct.
27. Excel’s __________ function can be used to compute the expected value of a discrete
random variable.
a. SUMPRODUCT
b. AVERAGE
c. MEDIAN
d. VAR
28. Variance is
a. a measure of the average, or central value of a random variable
b. a measure of the dispersion of a random variable
c. the square root of the standard deviation
d. the sum of the deviation of data elements from the mean
29. The variance is a weighted average of the
a. square root of the deviations from the mean
b. square root of the deviations from the median
c. squared deviations from the median
d. squared deviations from the mean
30. Excel’s __________ function can be used to compute the variance of a discrete random
variable.
a. SUMPRODUCT
b. AVERAGE
c. MEDIAN
d. VAR
31. The standard deviation is the
a. variance squared
b. square root of the sum of the deviations from the mean
c. same as the expected value
d. positive square root of the variance
32. x is a random variable with the probability function: f(x) = x/6 for x = 1,2 or 3.
The expected value of x is
a. 0.333
b. 0.500
c. 2.000
d. 2.333
Exhibit 5-1
The following represents the probability distribution for the daily demand of microcomputers at a
local store.
Demand
Probability
0
0.1
1
0.2
2
0.3
3
0.2
4
0.2
33. Refer to Exhibit 5-1. The expected daily demand is
a. 1.0
b. 2.2
c. 2
d. 4
34. Refer to Exhibit 5-1. The probability of having a demand for at least two
microcomputers is
a. 0.7
b. 0.3
c. 0.4
d. 1.0
Exhibit 5-2
The probability distribution for the daily sales at Michael’s Co. is given below.
Daily Sales ($1,000s)
Probability
40
0.1
50
0.4
60
0.3
70
0.2
35. Refer to Exhibit 5-2. The expected daily sales are
a. $55,000
b. $56,000
c. $50,000
d. $70,000
36. Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is
a. 0.5
b. 0.10
c. 0.30
d. 0.90
Exhibit 5-3
The probability distribution for the number of goals the Lions soccer team makes per game is
given below.
Number of Goals
Probability
0
0.05
1
0.15
2
0.35
3
0.30
4
0.15
37. Refer to Exhibit 5-3. The expected number of goals per game is
a. 0
b. 1
c. 2
d. 2.35
38. Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score at
least 1 goal?
a. 0.20
b. 0.55
c. 1.0
d. 0.95
39. Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score
less than 3 goals?
a. 0.85
b. 0.55
c. 0.45
d. 0.80
40. Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score no
goals?
a. 0.95
b. 0.85
c. 0.75
d. None of the answers is correct.
Exhibit 5-4
A local bottling company has determined the number of machine breakdowns per month and their
respective probabilities as shown below.
Number of
Breakdowns
Probability
0
0.12
1
0.38
2
0.25
3
0.18
4
0.07
41. Refer to Exhibit 5-4. The expected number of machine breakdowns per month is
a. 2
b. 1.70
c. one
d. None of the alternative answers is correct.
42. Refer to Exhibit 5-4. The probability of at least 3 breakdowns in a month is
a. 0.5
b. 0.10
c. 0.30
d. None of the alternative answers is correct.
43. Refer to Exhibit 5-4. The probability of no breakdowns in a month is
a. 0.88
b. 0.00
c. 0.50
d. None of the alternative answers is correct.
Exhibit 5-5
AMR is a computer-consulting firm. The number of new clients that they have obtained each
month has ranged from 0 to 6. The number of new clients has the probability distribution that is
shown below.
Number of
New Clients
Probability
0
0.05
1
0.10
2
0.15
3
0.35
4
0.20
5
0.10
6
0.05
44. Refer to Exhibit 5-5. The expected number of new clients per month is
a. 6
b. 0
c. 3.05
d. 21
45. Refer to Exhibit 5-5. The variance is
a. 1.431
b. 2.0475
c. 3.05
d. 21
46. Refer to Exhibit 5-5. The standard deviation is
a. 1.431
b. 2.047
c. 3.05
d. 21
47. The number of electrical outages in a city varies from day to day. Assume that the
number of electrical outages (x) in the city has the following probability distribution.
x
f(x)
0
0.80
1
0.15
2
0.04
3
0.01
The mean and the standard deviation for the number of electrical outages (respectively)
are
a. 2.6 and 5.77
b. 0.26 and 0.577
c. 3 and 0.01
d. 0 and 0.8
Exhibit 5-6
Probability Distribution
x
f(x)
10
.2
20
.3
30
.4
40
.1
48. Refer to Exhibit 5-6. The expected value of x equals
a. 24
b. 25
c. 30
d. 100
49. Refer to Exhibit 5-6. The variance of x equals
a. 9.165
b. 84
c. 85
d. 93.33
Exhibit 5-7
A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are
given the following sample information.
Cups of Coffee
Frequency
0
700
1
900
2
600
3
300
2,500
50. Refer to Exhibit 5-7. The expected number of cups of coffee is
a. 1
b. 1.2
c. 1.5
d. 1.7
51. Refer to Exhibit 5-7. The variance of the number of cups of coffee is
a. .96
b. .9798
c. 1
d. 2.4
52. Which of the following is a characteristic of a binomial experiment?
a. at least 2 outcomes are possible
b. the probability of success changes from trial to trial
c. the trials are independent
d. All of these answers are correct.
53. In a binomial experiment, the
a. probability of success does not change from trial to trial
b. probability of success does change from trial to trial
c. probability of success could change from trial to trial, depending on the situation
under consideration
d. All of these answers are correct.
54. Which of the following is not a characteristic of an experiment where the binomial
probability distribution is applicable?
a. the experiment has a sequence of n identical trials
b. exactly two outcomes are possible on each trial
c. the trials are dependent
d. the probabilities of the outcomes do not change from one trial to another
55. Which of the following is not a property of a binomial experiment?
a. the experiment consists of a sequence of n identical trials
b. each outcome can be referred to as a success or a failure
c. the probabilities of the two outcomes can change from one trial to the next
d. the trials are independent
56. A probability distribution showing the probability of x successes in n trials, where the
probability of success does not change from trial to trial, is termed a
a. uniform probability distribution
b. binomial probability distribution
c. hypergeometric probability distribution
d. normal probability distribution
57. The binomial probability distribution is used with
a. a continuous random variable
b. a discrete random variable
c. any distribution, as long as it is not normal
d. All of these answers are correct.
58. If you are conducting an experiment where the probability of a success is .02 and you are
interested in the probability of 4 successes in 15 trials, the correct probability function to
use is the
a. standard normal probability density function
b. normal probability density function
c. Poisson probability function
d. binomial probability function
59. In a binomial experiment the probability of success is 0.06. What is the probability of
two successes in seven trials?
a. 0.0036
b. 0.06
c. 0.0554
d. 0.28
60. Four percent of the customers of a mortgage company default on their payments. A
sample of five customers is selected. What is the probability that exactly two customers
in the sample will default on their payments?
a. 0.2592
b. 0.0142
c. 0.9588
d. 0.7408
61. A production process produces 2% defective parts. A sample of five parts from the
production process is selected. What is the probability that the sample contains exactly
two defective parts?
a. 0.0004
b. 0.0038
c. 0.10
d. 0.02
62. Excel’s BINOMDIST function can be used to compute
a. bin width for histograms
b. binomial probabilities
c. cumulative binomial probabilities
d. Both binomial probabilities and cumulative binomial probabilities are correct.
63. Excel’s BINOMDIST function has how many inputs?
a. 2
b. 3
c. 4
d. 5
64. When using Excel’s BINOMDIST function, one should choose TRUE for the fourth
input if
a. a probability is desired
b. a cumulative probability is desired
c. the expected value is desired
d. the correct answer is desired
65. The expected value for a binomial probability distribution is
a. E(x) = pn(1 − n)
b. E(x) = p(1 − p)
c. E(x) = np
d. E(x) = np(1 − p)
66. The variance for the binomial probability distribution is
a. Var(x) = p(1 − p)
b. Var(x) = np
c. Var(x) = n(1 − p)
d. Var(x) = np(1 − p)
67. The standard deviation of a binomial distribution is
a. E(x) = pn(1 − n)
b. E(x) = np(1 − p)
EMBS4 TB05 – 13
c. E(x) = np
d. None of the alternative answers is correct.
68. Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The
expected value of this distribution is
a. 0.50
b. 0.30
c. 50
d. Not enough information is given to answer this question.
69. Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The
variance of this distribution is
a. 20
b. 12
c. 3.46
d. Not enough information is given to answer this question.
70. Twenty percent of the students in a class of 100 are planning to go to graduate school.
The standard deviation of this binomial distribution is
a. 20
b. 16
c. 4
d. 2
Exhibit 5-8
The student body of a large university consists of 60% female students. A random sample of 8
students is selected.
71. Refer to Exhibit 5-8. What is the random variable in this experiment?
a. the 60% of female students
b. the random sample of 8 students
c. the number of female students out of 8
d. the student body size
72. Refer to Exhibit 5-8. What is the probability that among the students in the sample
exactly two are female?
a. 0.0896
b. 0.2936
c. 0.0413
d. 0.0007
73. Refer to Exhibit 5-8. What is the probability that among the students in the sample at
least 7 are female?
a. 0.1064
b. 0.0896
c. 0.0168
d. 0.8936
74. Refer to Exhibit 5-8. What is the probability that among the students in the sample at
least 6 are male?
a. 0.0413
b. 0.0079
c. 0.0007
d. 0.0499
Exhibit 5-9
Forty percent of all registered voters in a national election are female. A random sample of 5
voters is selected.
75. Refer to Exhibit 5-9. What is the random variable in this experiment?
a. the 40% of female registered voters
b. the random sample of 5 voters
c. the number of female voters out of 5
d. the number of registered voters in the nation
76. Refer to Exhibit 5-9. The probability that the sample contains 2 female voters is
a. 0.0778
b. 0.7780
c. 0.5000
d. 0.3456
77. Refer to Exhibit 5-9. The probability that there are no females in the sample is
a. 0.0778
b. 0.7780
c. 0.5000
d. 0.3456
Exhibit 5-10
The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is
going fishing 3 days next week.
78. Refer to Exhibit 5-10. What is the random variable in this experiment?
a. the 0.8 probability of catching fish
b. the 3 days
c. the number of days out of 3 that Pete catches fish
d. the number of fish in the body of water
79. Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is
a. .008
b. .096
c. .104
d. .8
80. Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is
a. .008
b. .096
c. .104
d. .8
81. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is
a. .6
b. .8
c. 2.4
d. 3
82. Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is
a. .16
b. .48
c. .8
d. 2.4
83. The Poisson probability distribution is a
a. continuous probability distribution
b. discrete probability distribution
c. uniform probability distribution
d. normal probability distribution
84. The Poisson probability distribution is used with
a. a continuous random variable
b. a discrete random variable
c. either a continuous or discrete random variable
d. any random variable
85. When dealing with the number of occurrences of an event over a specified interval of
time or space and when the occurrence or nonoccurrence in any interval is independent of
the occurrence or nonoccurrence in any other interval, the appropriate probability
distribution is a
a. binomial distribution
b. Poisson distribution
c. normal distribution
d. hypergeometric probability distribution
86. Excel’s POISSON function can be used to compute
a. bin width for histograms
b. Poisson probabilities
c. cumulative Poisson probabilities
d. Both Poisson probabilities and cumulative Poisson probabilities are correct.
87. Excel’s POISSON function has how many inputs?
a. 2
b. 3
c. 4
d. 5
88. When using Excel’s POISSON function, one should choose TRUE for the third input if
a. a probability is desired
b. a cumulative probability is desired
c. the expected value is desired
d. the correct answer is desired
89. In the textile industry, a manufacturer is interested in the number of blemishes or flaws
occurring in each 100 feet of material. The probability distribution that has the greatest
chance of applying to this situation is the
a. normal distribution
b. binomial distribution
c. Poisson distribution
Exhibit 5-11
The random variable x is the number of occurrences of an event over an interval of ten minutes.
It can be assumed that the probability of an occurrence is the same in any two time periods of an
equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
90. Refer to Exhibit 5-11. The random variable x satisfies which of the following probability
distributions?
a. normal
b. Poisson
c. binomial
d. Not enough information is given to answer this question.
91. Refer to Exhibit 5-11. The appropriate probability distribution for the random variable is
a. discrete
b. continuous
c. either a or b depending on how the interval is defined
d. not enough information is given
92. Refer to Exhibit 5-11. The expected value of the random variable x is
a. 2
b. 5.3