Contemporary Business Statistics International Edition 4th Edition by Thomas A. Williams - Test Bank

Contemporary Business Statistics International Edition 4th Edition by Thomas A. Williams – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

CHAPTER 5—DISCRETE PROBABILITY DISTRIBUTIONS

 

MULTIPLE CHOICE

 

1. A numerical description of the outcome of an experiment is called a

a.	descriptive statistic
b.	probability function
c.	variance
d.	random variable

 

 

ANS:  D                    PTS:   1

 

2. 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

 

 

ANS:  C                    PTS:   1

 

3. 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

 

 

ANS:  A                    PTS:   1

 

4. 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.

 

 

ANS:  A                    PTS:   1

 

5. 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

 

 

ANS:  B                    PTS:   1

 

 

6. 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.

 

 

ANS:  B                    PTS:   1

 

7. 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

 

 

ANS:  A                    PTS:   1

 

8. 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

 

 

ANS:  B                    PTS:   1

 

9. 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

 

 

ANS:  A                    PTS:   1

 

10. Which of the following is(are) required condition(s) for a discrete probability function?

a.	åf(x) = 0
b.	f(x) ³ 1 for all values of x
c.	f(x) < 0
d.	None of the answers is correct.

 

 

ANS:  D                    PTS:   1

 

11. Which of the following is not a required condition for a discrete probability function?

a.	f(x) ³ 0 for all values of x
b.	åf(x) = 1
c.	åf(x) = 0
d.	All of the answers are correct.

 

 

ANS:  C                    PTS:   1

 

 

12. 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 åf(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.

 

 

ANS:  C                    PTS:   1

 

13. 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.

 

 

ANS:  C                    PTS:   1

 

14. 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

 

 

ANS:  C                    PTS:   1

 

15. 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.

 

 

ANS:  D                    PTS:   1

 

16. 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.

 

 

ANS:  C                    PTS:   1

 

17. Excel’s __________ function can be used to compute the expected value of a discrete random variable.

a.	SUMPRODUCT
b.	AVERAGE
c.	MEDIAN
d.	VAR

 

 

ANS:  A                    PTS:   1

 

 

18. 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

 

 

ANS:  B                    PTS:   1

 

19. 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

 

 

ANS:  D                    PTS:   1

 

20. Excel’s __________ function can be used to compute the variance of a discrete random variable.

a.	SUMPRODUCT
b.	AVERAGE
c.	MEDIAN
d.	VAR

 

 

ANS:  A                    PTS:   1

 

21. 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

 

 

ANS:  D                    PTS:   1

 

22. 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

 

 

ANS:  D                    PTS:   1

 

23. 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

 

 

ANS:  B                    PTS:   1

 

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

 

 

24. Refer to Exhibit 5-1. The expected daily demand is

a.	1.0
b.	2.2
c.	2
d.	4

 

 

ANS:  B                    PTS:   1

 

25. 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

 

 

ANS:  A                    PTS:   1

 

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

 

 

26. Refer to Exhibit 5-2. The expected daily sales are

a.	$55,000
b.	$56,000
c.	$50,000
d.	$70,000

 

 

ANS:  B                    PTS:   1

 

27. 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

 

 

ANS:  D                    PTS:   1

 

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

 

 

28. Refer to Exhibit 5-3. The expected number of goals per game is

a.	0
b.	1
c.	2
d.	2.35

 

 

ANS:  D                    PTS:   1

 

29. 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

 

 

ANS:  D                    PTS:   1

 

30. 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

 

 

ANS:  B                    PTS:   1

 

31. 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.

 

 

ANS:  D                    PTS:   1

 

 

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

 

 

32. 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.

 

 

ANS:  B                    PTS:   1

 

33. 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.

 

 

ANS:  D                    PTS:   1

 

34. 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.

 

 

ANS:  D                    PTS:   1

 

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

 

 

 

35. Refer to Exhibit 5-5. The expected number of new clients per month is

a.	6
b.	0
c.	3.05
d.	21

 

 

ANS:  C                    PTS:   1

 

36. Refer to Exhibit 5-5. The variance is

a.	1.431
b.	2.0475
c.	3.05
d.	21

 

 

ANS:  B                    PTS:   1

 

37. Refer to Exhibit 5-5. The standard deviation is

a.	1.431
b.	2.047
c.	3.05
d.	21

 

 

ANS:  A                    PTS:   1

 

Exhibit 5-6

Probability Distribution

 

	x	f(x)
	10	.2
	20	.3
	30	.4
	40	.1

 

 

38. Refer to Exhibit 5-6. The expected value of x equals

a.	24
b.	25
c.	30
d.	100

 

 

ANS:  A                    PTS:   1

 

39. Refer to Exhibit 5-6. The variance of x equals

a.	9.165
b.	84
c.	85
d.	93.33

 

 

ANS:  B                    PTS:   1

 

 

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

 

 

40. Refer to Exhibit 5-7. The expected number of cups of coffee is

a.	1
b.	1.2
c.	1.5
d.	1.7

 

 

ANS:  B                    PTS:   1

 

41. Refer to Exhibit 5-7. The variance of the number of cups of coffee is

a.	.96
b.	.9798
c.	1
d.	2.4

 

 

ANS:  A                    PTS:   1

 

42. 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.

 

 

ANS:  C                    PTS:   1

 

43. 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.

 

 

ANS:  A                    PTS:   1

 

44. 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

 

 

ANS:  C                    PTS:   1

 

45. 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

 

 

ANS:  C                    PTS:   1

 

46. 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

 

 

ANS:  B                    PTS:   1

 

47. 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.

 

 

ANS:  B                    PTS:   1

 

48. 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

 

 

ANS:  D                    PTS:   1

 

49. 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

 

 

ANS:  C                    PTS:   1

 

50. 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

 

 

ANS:  B                    PTS:   1

 

51. 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

 

 

ANS:  B                    PTS:   1

 

52. Excel’s BINOM.DIST 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.

 

 

ANS:  D                    PTS:   1

 

53. Excel’s BINOM.DIST function has how many inputs?

a.	2
b.	3
c.	4
d.	5

 

 

ANS:  C                    PTS:   1

 

54. When using Excel’s BINOM.DIST 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

 

 

ANS:  B                    PTS:   1

 

55. 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)

 

 

ANS:  C                    PTS:   1

 

56. 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)

 

 

ANS:  D                    PTS:   1

 

 

57. The standard deviation of a binomial distribution is

a.	E(x) = pn(1 – n)
b.	E(x) = np(1 – p)
c.	E(x) = np
d.	None of the alternative answers is correct.

 

 

ANS:  D                    PTS:   1

 

58. 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.

 

 

ANS:  C                    PTS:   1

 

59. 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.

 

 

ANS:  B                    PTS:   1

 

60. 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

 

 

ANS:  C                    PTS:   1

 

Exhibit 5-8

The student body of a large university consists of 60% female students. A random sample of 8 students is selected.

 

61. 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

 

 

ANS:  C                    PTS:   1

 

 

62. 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

 

 

ANS:  C                    PTS:   1

 

63. 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

 

 

ANS:  A                    PTS:   1

 

64. 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

 

 

ANS:  D                    PTS:   1

 

Exhibit 5-9

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.

 

65. 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

 

 

ANS:  C                    PTS:   1

 

66. 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

 

 

ANS:  D                    PTS:   1

 

67. 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

 

 

ANS:  A                    PTS:   1

 

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.

 

68. 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

 

 

ANS:  C                    PTS:   1

 

69. 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

 

 

ANS:  B                    PTS:   1

 

70. 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

 

 

ANS:  C                    PTS:   1

 

71. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is

a.	.6
b.	.8
c.	2.4
d.	3

 

 

ANS:  C                    PTS:   1

 

72. 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

 

 

ANS:  B                    PTS:   1

 

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.

 

 

73. 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.

 

 

ANS:  B                    PTS:   1

 

74. 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

 

 

ANS:  A                    PTS:   1

 

75. Refer to Exhibit 5-11. The expected value of the random variable x is

a.	2
b.	5.3
c.	10
d.	2.30

 

 

ANS:  B                    PTS:   1

 

76. Refer to Exhibit 5-11. The probability that there are 8 occurrences in ten minutes is

a.	.0241
b.	.0771
c.	.1126
d.	.9107

 

 

ANS:  B                    PTS:   1

 

77. Refer to Exhibit 5-11. The probability that there are less than 3 occurrences is

a.	.0659
b.	.0948
c.	.1016
d.	.1239

 

 

ANS:  C                    PTS:   1

 

78. The Poisson probability distribution is a

a.	continuous probability distribution
b.	discrete probability distribution
c.	uniform probability distribution
d.	normal probability distribution

 

 

ANS:  B                    PTS:   1

 

 

79. 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

 

 

ANS:  B                    PTS:   1

 

80. 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

 

 

ANS:  B                    PTS:   1

 

81. Excel’s POISSON.DIST 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.

 

 

ANS:  D                    PTS:   1

 

82. Excel’s POISSON.DIST function has how many inputs?

a.	2
b.	3
c.	4
d.	5

 

 

ANS:  B                    PTS:   1

 

83. When using Excel’s POISSON.DIST 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

 

 

ANS:  B                    PTS:   1

 

84. 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
d.	uniform distribution

 

 

ANS:  C                    PTS:   1

 

 

85. When sampling without replacement, the probability of obtaining a certain sample is best given by a

a.	hypergeometric distribution
b.	binomial distribution
c.	Poisson distribution
d.	normal distribution

 

 

ANS:  A                    PTS:   1

 

86. The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution the

a.	probability of success must be less than 0.5
b.	probability of success changes from trial to trial
c.	trials are independent of each other
d.	random variable is continuous

 

 

ANS:  B                    PTS:   1

 

87. Excel’s HYPGEOM.DIST function can be used to compute

a.	bin width for histograms
b.	hypergeometric probabilities
c.	cumulative hypergeometric probabilities
d.	Both hypergeometric probabilities and cumulative hypergeometric probabilities are correct.

 

 

ANS:  B                    PTS:   1

 

88. Excel’s HYPGEOM.DIST function has how many inputs?

a.	2
b.	3
c.	4
d.	5

 

 

ANS:  D                    PTS:   1

 

89. When using Excel’s HYPGEOM.DIST function, one should choose TRUE for the fifth input if

a.	a probability is desired
b.	a cumulative probability is desired
c.	the expected value is desired
d.	None of the alternative answers is correct.

 

 

ANS:  B                    PTS:   1

 

90. 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

 

 

ANS:  D                    PTS:   1

 

 

91. 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

 

 

ANS:  B                    PTS:   1

 

92. The _____ probability function is based in part on the counting rule for combinations.

a.	binomial
b.	Poisson
c.	hypergeometric
d.	exponential

 

 

ANS:  C                    PTS:   1

 

93. 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

 

 

ANS:  C                    PTS:   1

 

94. 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

 

 

ANS:  B                    PTS:   1

 

95. Which of the following properties of a binomial experiment is called the stationarity

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

 

 

ANS:  C                    PTS:   1

 

96. 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

 

 

ANS:  C                    PTS:   1

 

 

97. 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

 

 

ANS:  D                    PTS:   1

 

98. 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

 

 

ANS:  C                    PTS:   1

 

99. A binomial probability distribution with p = .3 is

a.	negatively skewed
b.	symmetrical
c.	positively skewed
d.	bimodal

 

 

ANS:  A                    PTS:   1

 

PROBLEM

 

1. The probability distribution for the rate of return on an investment is

 

	Rate of Return (%)	Probability
	9.5	.1
	9.8	.2
	10.0	.3
	10.2	.3
	10.6	.1

 

a.	What is the probability that the rate of return will be at least 10%?
b.	What is the expected rate of return?
c.	What is the variance of the rate of return?

 

 

ANS:

a.	0.7
b.	10.03
c.	0.0801

 

 

PTS:   1

 

 

2. A random variable x has the following probability distribution:

 

	x	f(x)
	0	0.08
	1	0.17
	2	0.45
	3	0.25
	4	0.05

 

a.	Determine the expected value of x.
b.	Determine the variance.

 

 

ANS:

a.	2.02
b.	0.9396

 

 

PTS:   1

 

3. For the following probability distribution:

 

	x	f(x)
	0	0.01
	1	0.02
	2	0.10
	3	0.35
	4	0.20
	5	0.11
	6	0.08
	7	0.05
	8	0.04
	9	0.03
	10	0.01

 

a.	Determine E(x).
b.	Determine the variance and the standard deviation.

 

 

ANS:

a.	4.14
b.	variance = 3.7   std. dev. = 1.924

 

 

PTS:   1

 

 

4. A company sells its products to wholesalers in batches of 1,000 units only. The daily demand for its product and the respective probabilities are given below.

 

	Demand (Units)	Probability
	0	0.2
	1000	0.2
	2000	0.3
	3000	0.2
	4000	0.1

 

a.	Determine the expected daily demand.
b.	Assume that the company sells its product at $3.75 per unit. What is the expected daily revenue?

 

 

ANS:

a.	1800
b.	$6,750

 

 

PTS:   1

 

5. The demand for a product varies from month to month. Based on the past year’s data, the following probability distribution shows MNM company’s monthly demand.

 

	x	f(x)
	Unit Demand	Probability
	0	0.10
	1,000	0.10
	2,000	0.30
	3,000	0.40
	4,000	0.10

 

a.	Determine the expected number of units demanded per month.
b.	Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units?

 

 

ANS:

a.	2300
b.	Profit = $1600

 

 

PTS:   1

 

 

6. The probability distribution of the daily demand for a product is shown below.

 

	Demand	Probability
	0	0.05
	1	0.10
	2	0.15
	3	0.35
	4	0.20
	5	0.10
	6	0.05

 

a.	What is the expected number of units demanded per day?
b.	Determine the variance and the standard deviation.

 

 

ANS:

a.	3.05
b.	variance = 2.0475     std. dev. = 1.431

 

 

PTS:   1

 

7. The random variable x has the following probability distribution:

 

	x	f(x)
	0	.25
	1	.20
	2	.15
	3	.30
	4	.10

 

a.	Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b.	Calculate the expected value of x.
c.	Calculate the variance of x.
d.	Calculate the standard deviation of x.

 

 

ANS:

a.	yes f(x) ³ 0 and åf(x) = 1
b.	1.8
c.	1.86
d.	1.364

 

 

PTS:   1

 

 

8. The probability function for the number of insurance policies John will sell to a customer is given by

f(x) = .5 – (x/6) for x = 0, 1, or 2

 

a.	Is this a valid probability function? Explain your answer.
b.	What is the probability that John will sell exactly 2 policies to a customer?
c.	What is the probability that John will sell at least 2 policies to a customer?
d.	What is the expected number of policies John will sell?
e.	What is the variance of the number of policies John will sell?

 

 

ANS:

a.	yes f(x) ³ 0 and åf(x) = 1
b.	0.167
c.	0.167
d.	0.667
e.	0.556

 

 

PTS:   1

 

9. Thirty-two percent of the students in a management class are graduate students. A random sample of 5 students is selected. Using the binomial probability function, determine the probability that the sample contains exactly 2 graduate students?

 

ANS:

0.322 (rounded)

 

PTS:   1

 

10. A production process produces 2% defective parts. A sample of 5 parts from the production is selected. What is the probability that the sample contains exactly two defective parts? Use the binomial probability function and show your computations to answer this question.

 

ANS:

0.0037648

 

PTS:   1

 

11. When a particular machine is functioning properly, 80% of the items produced are non-defective. If three items are examined, what is the probability that one is defective? Use the binomial probability function to answer this question.

 

ANS:

0.384

 

PTS:   1

 

12. The records of a department store show that 20% of its customers who make a purchase return the merchandise in order to exchange it. In the next six purchases,

a.	what is the probability that three customers will return the merchandise for exchange?
b.	what is the probability that four customers will return the merchandise for exchange?
c.	what is the probability that none of the customers will return the merchandise for exchange?

 

 

ANS:

a.	0.0819
b.	0.0154
c.	0.2621

 

 

PTS:   1

 

13. Ten percent of the items produced by a machine are defective. Out of 15 items chosen at random,

a.	what is the probability that exactly 3 items will be defective?
b.	what is the probability that less than 3 items will be defective?
c.	what is the probability that exactly 11 items will be non-defective?

 

 

ANS:

a.	0.1285
b.	0.816
c.	0.0428

 

 

PTS:   1

 

14. In a large university, 15% of the students are female. If a random sample of twenty students is selected,

a.	what is the probability that the sample contains exactly four female students?
b.	what is the probability that the sample will contain no female students?
c.	what is the probability that the sample will contain exactly twenty female students?
d.	what is the probability that the sample will contain more than nine female students?
e.	what is the probability that the sample will contain fewer than five female students?
f.	what is the expected number of female students?

 

 

ANS:

a.	0.1821
b.	0.0388
c.	0.0000
d.	0.0002
e.	0.8298
f.	3

 

 

PTS:   1

 

15. Seventy percent of the students applying to a university are accepted. What is the probability that among the next 18 applicants

a.	At least 6 will be accepted?
b.	Exactly 10 will be accepted?
c.	Exactly 5 will be rejected?
d.	Fifteen or more will be accepted?
e.	Determine the expected number of acceptances.
f.	Compute the standard deviation.

 

 

 

ANS:

a.	0.9988
b.	0.0811
c.	0.2017
d.	0.1646
e.	12.6
f.	1.9442

 

 

PTS:   1

 

16. Twenty percent of the applications received for a particular position are rejected. What is the probability that among the next fourteen applications,

a.	none will be rejected?
b.	all will be rejected?
c.	less than 2 will be rejected?
d.	more than four will be rejected?
e.	Determine the expected number of rejected applications and its variance.

 

 

ANS:

a.	0.0440
b.	0.0000
c.	0.1979
d.	0.1298
e.	2.8, 2.24

 

 

PTS:   1

 

17. Fifty-five percent of the applications received for a particular credit card are accepted. Among the next twelve applications,

a.	what is the probability that all will be rejected?
b.	what is the probability that all will be accepted?
c.	what is the probability that exactly 4 will be accepted?
d.	what is the probability that fewer than 3 will be accepted?
e.	Determine the expected number and the variance of the accepted applications.

 

 

ANS:

a.	0.0001
b.	0.0008
c.	0.0762
d.	0.0079
e.	6.60; 2.9700

 

 

PTS:   1

 

18. In a southern state, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station,

a.	what is the probability that none will pass inspection?
b.	what is the probability that all will pass inspection?
c.	what is the probability that exactly two will not pass inspection?
d.	what is the probability that more than three will not pass inspection?
e.	what is the probability that fewer than two will not pass inspection?
f.	Find the expected number of automobiles not passing inspection.
g.	Determine the standard deviation for the number of cars not passing inspection.

 

 

ANS:

a.	0.0000
b.	0.5987
c.	0.0746
d.	0.0010
e.	0.9139
f.	0.5
g.	0.6892

 

 

PTS:   1

 

19. Only 0.02% of credit card holders of a company report the loss or theft of their credit cards each month. The company has 15,000 credit cards in the city of Memphis. What is the probability that during the next month in the city of Memphis

a.	no one reports the loss or theft of their credit cards?
b.	every credit card is lost or stolen?
c.	six people report the loss or theft of their cards?
d.	at least nine people report the loss or theft of their cards?
e.	Determine the expected number of reported lost or stolen credit cards.
f.	Determine the standard deviation for the number of reported lost or stolen cards.

 

 

ANS:

a.	0.0498
b.	0.0000
c.	0.0504
d.	0.0038
e.	3
f.	1.73

 

 

PTS:   1

 

20. Two percent of the parts produced by a machine are defective. Forty parts are selected. Define the random variable x to be the number of defective parts.

a.	What is the probability that exactly 3 parts will be defective?
b.	What is the probability that the number of defective parts will be more than 2 but fewer than 6?
c.	What is the probability that fewer than 4 parts will be defective?
d.	What is the expected number of defective parts?
e.	What is the variance for the number of defective parts?

 

 

ANS:

a.	0.0374
b.	0.0455
c.	0.9918
d.	0.8
e.	0.784

 

 

PTS:   1

 

21. A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is 0.1. Define a random variable x to be the number of machines that will break down in a day.

a.	What is the appropriate probability distribution for x? Explain how x satisfies the properties of the distribution.
b.	Compute the probability that 4 machines will break down.
c.	Compute the probability that at least 4 machines will break down.
d.	What is the expected number of machines that will break down in a day?
e.	What is the variance of the number of machines that will break down in a day?

 

 

ANS:

a.	binomial
b.	0.0004
c.	0.0004
d.	0.5
e.	0.45

 

 

PTS:   1

 

22. In a large corporation, 65% of the employees are male. A random sample of five employees is selected.

a.	Define the random variable in words for this experiment.
b.	What is the probability that the sample contains exactly three male employees?
c.	What is the probability that the sample contains no male employees?
d.	What is the probability that the sample contains more than three female employees?
e.	What is the expected number of female employees in the sample?

 

 

ANS:

a.	x = the number of male employees out of 5
b.	0.3364
c.	0.0053
d.	0.0541
e.	1.75

 

 

PTS:   1

 

23. In a large university, 75% of students live in the dormitories. A random sample of 5 students is selected.

a.	Define the random variable in words for this experiment.
b.	What is the probability that the sample contains exactly three students who live in the dormitories?
c.	What is the probability that the sample contains no students who live in the dormitories?
d.	What is the probability that the sample contains more than three students who do not live in the dormitories?
e.	What is the expected number of students (in the sample) who do not live in the dormitories?

 

 

 

ANS:

a.	x = the number of students out of 5 who live in the dormitories
b.	0.2637
c.	0.001
d.	0.0156
e.	1.25

 

 

PTS:   1

 

24. A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected.

a.	Define the random variable in words for this experiment.
b.	What is the probability that the sample will contain 7 non-defective parts?
c.	What is the probability that the sample will contain at least 4 defective parts?
d.	What is the probability that the sample will contain less than 5 non-defective parts?
e.	What is the probability that the sample will contain no defective parts?

 

 

ANS:

a.	x = the number of non-defective parts out of 10
b.	0.0574
c.	0.0128
d.	0.0001
e.	0.3487

 

 

PTS:   1

 

25. The student body of a large university consists of 30% Business majors. A random sample of 20 students is selected.

a.	Define the random variable in words for this experiment.
b.	What is the probability that among the students in the sample at least 10 are Business majors?
c.	What is the probability that at least 16 are not Business majors?
d.	What is the probability that exactly 10 are Business majors?
e.	What is the probability that exactly 12 are not Business majors?

 

 

ANS:

a.	x = the number of students out of 20 who are Business majors
b.	0.0480
c.	0.2375
d.	0.0308
e.	0.1144

 

 

PTS:   1

 

26. A local university reports that 3% of their students take their general education courses on a pass/fail basis. Assume that fifty students are registered for a general education course.

a.	Define the random variable in words for this experiment.
b.	What is the expected number of students who have registered on a pass/fail basis?
c.	What is the probability that exactly five are registered on a pass/fail basis?
d.	What is the probability that more than three are registered on a pass/fail basis?
e.	What is the probability that less than four are registered on a pass/fail basis?

 

 

ANS:

a.	x = the number of student out of 50 who are registered for a general education course
b.	1.5
c.	0.0131
d.	0.0628
e.	0.9372

 

 

PTS:   1

 

27. Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected.

a.	Define the random variable in words for this experiment.
b.	What is the probability that the sample contains exactly 4 minorities?
c.	What is the probability that the sample contains fewer than 2 minorities?
d.	What is the probability that the sample contains exactly 1 non-minority?
e.	What is the expected number of minorities in the sample?
f.	What is the variance of the minorities?

 

 

ANS:

a.	x = the number of minority employees out of 7
b.	0.0577
c.	0.4449
d.	0.0013
e.	1.75
f.	1.3125

 

 

PTS:   1

 

28. Twenty-five percent of all resumes received by a corporation for a management position are from females. Fifteen resumes will be received tomorrow.

a.	Define the random variable in words for this experiment.
b.	What is the probability that exactly 5 of the resumes will be from females?
c.	What is the probability that fewer than 3 of the resumes will be from females?
d.	What is the expected number of resumes from women?
e.	What is the variance of the number of resumes from women?

 

 

ANS:

a.	x = the number of resumes out of 15 that are from females
b.	0.1651
c.	0.2361
d.	3.75
e.	2.8125

 

 

PTS:   1

 

29. A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is 0.10.

a.	Define the random variable in words for this experiment.
b.	What is the probability the salesperson will make exactly two sales in a day?
c.	What is the probability the salesperson will make at least two sales in a day?
d.	What percentage of days will the salesperson not make a sale?
e.	What is the expected number of sales per day?

 

 

ANS:

a.	x = the number of sales made out of 8 contacts
b.	0.1488
c.	0.1869
d.	43.05%
e.	0.8

 

 

PTS:   1

 

30. An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch. What is the probability that during the next week

a.	exactly seven claims will be filed?
b.	no claims will be filed?
c.	less than four claims will be filed?
d.	at least eighteen claims will be filed?

 

 

ANS:

a.	0.1171
b.	0.0001
c.	0.0212
d.	0.0053

 

 

PTS:   1

 

31. John parks cars at a hotel. On the average, 6.7 cars will arrive in an hour. Assume that a driver’s decision on whether to let John park the car does not depend upon any other person’s decision. Define the random variable x to be the number of cars arriving in any hour period.

a.	What is the appropriate probability distribution for x? Explain how x satisfies the properties of the distribution.
b.	Compute the probability that exactly 5 cars will arrive in the next hour.
c.	Compute the probability that no more than 5 cars will arrive in the next hour.

 

 

ANS:

a.	Poisson
b.	0.1385
c.	0.3406

 

 

PTS:   1

 

32. The average number of calls received by a switchboard in a 30-minute period is 15.

a.	Define the random variable in words for this experiment.
b.	What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls?
c.	What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls?
d.	What is the probability that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?

 

 

ANS:

a.	x = the number of calls received in a 30-minute period
b.	0.0486
c.	0.3958
d.	0.0076

 

 

PTS:   1

 

33. A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch.

a.	Define the random variable in words for this experiment.
b.	What is the probability that during the next week exactly seven claims will be filed?
c.	What is the probability that during the next week no claims will be filed?
d.	What is the probability that during the next week fewer than four claims will be filed?
e.	What is the probability that during the next week at least seventeen claims will be filed?

 

 

ANS:

a.	x = the number of claims filed in a one-week period
b.	0.1490
c.	0.0009
d.	0.0818
e.	0.0010

 

 

PTS:   1

 

34. General Hospital has noted that they admit an average of 8 patients per hour.

a.	Define the random variable in words for this experiment.
b.	What is the probability that during the next hour fewer then 3 patients will be admitted?
c.	What is the probability that during the next two hours exactly 8 patients will be admitted?

 

 

ANS:

a.	x = the number of patients admitted per hour
b.	0.0137
c.	0.0120

 

 

PTS:   1

 

35. Shoppers enter Hamilton Place Mall at an average of 120 per hour.

a.	Define the random variable in words for this experiment.
b.	What is the probability that exactly 5 shoppers will enter the mall between noon and 1:00 p.m.?
c.	What is the probability that exactly 5 shoppers will enter the mall between noon and 12:05 p.m.?
d.	What is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10 p.m.?

 

 

 

ANS:

a.	x = the number of shoppers entering the mall in a one-hour period
b.	0.0000
c.	0.0378
d.	0.0015

 

 

PTS:   1

 

36. Compute the hypergeometric probabilities for the following values of n and x. Assume N = 8 and r = 5.

a.	n = 5, x = 2
b.	n = 6, x = 4
c.	n = 3, x = 0
d.	n = 3, x = 3

 

 

ANS:

a.	0.1786
b.	0.5357
c.	0.01786
d.	0.1786

 

 

PTS:   1

 

37. A retailer of electronic equipment received six HDTVs from the manufacturer. Three of the HDTVs were damaged in the shipment. The retailer sold two HDTVs to two customers.

a	Can a binomial formula be used for the solution of the above problem?
b.	What kind of probability distribution does the above satisfy, and is there a function for solving such problems?
c.	What is the probability that both customers received damaged HDTVs?
d.	What is the probability that one of the two customers received a defective HDTV?

 

 

ANS:

a.	No, in a binomial experiment, trials are independent of each other.
b.	Hypergeometric probability distribution
c.	0.2
d.	0.6

 

 

PTS:   1

 

38. Waters’ Edge is a clothing retailer that promotes its products via catalog and accepts customer orders by all of the conventional ways including the Internet.   The company has gained a competitive advantage by collecting data about its operations and the customer each time an order is processed.

 

Among the data collected with each order are: number of items ordered, total shipping weight of the order, whether or not all items ordered were available in inventory, time taken to process the order, customer’s number of prior orders in the last 12 months, and method of payment.  For each of the six aforementioned variables, identify which of the variables are discrete and which are continuous.

 

 

ANS:

Discrete:  number of items ordered, whether or not all items ordered were available in inventory, customer’s number of prior orders in the last 12 months, method of payment

Continuous:  total shipping weight of the order, time taken to process the order

 

PTS:   1

 

39. June’s Specialty Shop sells designer original dresses.  On 10% of her dresses, June makes a profit of $10, on 20% of her dresses she makes a profit of $20, on 30% of her dresses she makes a profit of $30, and on 40% of her dresses she makes a profit of $40.  On a given day, the probability of June having no customers is .05, of one customer is .10, of two customers is .20, of three customers is .35, of four customers is .20, and of five customers is .10.
40. What is the expected profit June earns on the sale of a dress?
41. June’s daily operating cost is $40 per day. Find the expected net profit June earns per day.  (Hint:  To find the expected daily gross profit, multiply the expected profit per dress by the expected number of customers per day.)
42. June is considering moving to a larger store. She estimates that doing so will double the expected number of customers.  If the larger store will increase her operating costs to $100 per day, should she make the move?

 

ANS:

1. $30
2. $45.50
3. Yes; new daily net profit expected is $71

 

PTS:   1

 

40. The salespeople at Gold Key Realty sell up to 9 houses per month. The probability distribution of a salesperson selling x houses in a month is as follows:

 

Sales (x)	0	1	2	3	4	5	6	7	8	9
Probability f (x)	.05	.10	.15	.20	.15	.10	.10	.05	.05	.05

1. What are the mean and standard deviation for the number of houses sold by a salesperson per month?
2. Any salesperson selling more houses than the amount equal to the mean plus two standard deviations receives a bonus. How many houses per month must a salesperson sell to receive a bonus?

 

ANS:

3. mean = 3.9, standard deviation = 2.34
4. 8.58 or 9 houses

 

PTS:   1

 

41. Sandy’s Pet Center grooms large and small dogs.  It takes Sandy 40 minutes to groom a small dog and 70 minutes to groom a large dog.  Large dogs account for 20% of Sandy’s business.  Sandy has 5 appointments tomorrow.
42. What is the probability that all 5 appointments tomorrow are for small dogs?
43. What is the probability that two of the appointments tomorrow are for large dogs?
44. What is the expected amount of time to finish all five dogs tomorrow?

 

ANS:

1. .3277
2. .2048
3. 230 minutes

 

PTS:   1

 

42. Ralph’s Gas Station is running a giveaway promotion.  With every fill-up of gasoline, Ralph gives out a lottery ticket that has a 25% chance of being a winning ticket.  Customers who collect four winning lottery tickets are eligible for the “BIG SPIN” for large payoffs.  What is the probability of qualifying for the big spin if a customer fills up: (a) 3 times; (b) 4 times; (c) 7 times?

 

ANS:

1. 0
2. .0039
3. .0705

 

PTS:   1

 

43. The number of customers at Winkies Donuts between 8:00a.m. and 9:00a.m. is believed to follow a Poisson distribution with a mean of 2 customers per minute.
44. During a randomly selected one-minute interval during this time period, what is the probability of 6 customers arriving to Winkies?
45. What is the probability that at least 2 minutes elapse between customer arrivals?

 

ANS:

1. .0120
2. .0183

 

PTS:   1

 

44. During lunchtime, customers arrive at Bob’s Drugs according to a Poisson distribution with     l = 4 per minute.
45. During a one minute interval, determine the following probabilities: (1) no arrivals; (2) one arrival; (3) two arrivals; and, (4) three or more arrivals.
46. What is the probability of two arrivals in a two-minute period?

 

ANS:

1. (1) .0183, (2) .0733, (3) .1465, (4) .7619
2. .0107

 

PTS:   1

 

45. Telephone calls arrive at the Global Airline reservation office in Louisville according to a Poisson distribution with a mean of 1.2 calls per minute.
46. What is the probability of receiving exactly one call during a one-minute interval?
47. What is the probability of receiving at most 2 calls during a one-minute interval?
48. What is the probability of receiving at least two calls during a one-minute interval?
49. What is the probability of receiving exactly 4 calls during a five-minute interval?
50. What is the probability that at most 2 minutes elapse between one call and the next?

 

ANS:

1. .36
2. .88
3. .34
4. .135
5. .9093

 

PTS:   1

 

46. Before dawn Josh hurriedly packed some clothes for a job-interview trip while his roommate was still sleeping.  He reached in his disorganized sock drawer where there were five black socks and five navy blue socks, although they appeared to be the same color in the dimly lighted room.  Josh grabbed six socks, hoping that at least two, and preferably four, of them were black to match the gray suit he had packed.  With no time to spare, he then raced to the airport to catch his plane.
47. What is the probability that Josh packed at least two black socks so that he will be dressed appropriately the day of his interview?
48. What is the probability that Josh packed at least four black socks so that he will be dressed appropriately the latter day of his trip as well?

 

ANS:

1. .976
2. .262

 

PTS:   1