ch5 problems

32. 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. 100 d. 50

D

44. 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

D

50. Refer to Exhibit 5-2. 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

D

70. Refer to Exhibit 5-9. The probability of having sales of at least $50,000 is a. 0.5 b. 0.10 c. 0.30 d. 0.90

D

72. Refer to Exhibit 5-10. 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

D

76. Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is a. 0.93 b. 0.88 c. 0.75 d. 0.25

D

42. 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. 144

B

52. Refer to Exhibit 5-3. The variance is a. 1.431 b. 2.047 c. 3.05 d. 21

B

57. Refer to Exhibit 5-5. The variance of x equals a. 9.165 b. 84 c. 85 d. 93.33

B

63. Refer to Exhibit 5-7. The variance of the number of days Pete will catch fish is a. .16 b. .48 c. .8 d. 2.4

B

66. Refer to Exhibit 5-8. The expected value of the random variable x is a. 2 b. 5.3 c. 10 d. 2.30

B

74. Refer to Exhibit 5-10. What is the probability that in a given game the Lions will score no goals? a. 0.95 b. 0.05 c. 0.75 d. 0.60

B

79. Refer to Exhibit 5-12. What is the probability that in a given day there will be at least 1 accident? a. 0.15 b. 0.85 c. at least 1 d. 0.5

B

Exhibit 5-6 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 58. Refer to Exhibit 5-6. The expected number of cups of coffee is a. 1 b. 1.2 c. 1.5 d. 1.7

B

21. 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

C

38. 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

B

47. Refer to Exhibit 5-1. The probability of having a demand for at least two computers is a. 0.7 b. 0.3 c. 0.4 d. 1.0

A

49. Refer to Exhibit 5-2. 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

A

53. Refer to Exhibit 5-3. The standard deviation is a. 1.431 b. 2.047 c. 3.05 d. 21

A

55. Refer to Exhibit 5-4. The probability that there are no females in the sample is a. 0.0778 b. 0.7780 c. 0.5000 d. 0.3456

A

59. Refer to Exhibit 5-6. The variance of the number of cups of coffee is a. .96 b. .9798 c. 1 d. 2.4

A

Exhibit 5-5 Probability Distribution x f(x) 10 .2 20 .3 30 .4 40 .1 56. Refer to Exhibit 5-5. The expected value of x equals a. 24 b. 25 c. 30 d. 100

A

67. Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is a. .0241 b. .0771 c. .1126 d. .9107

B

73. Refer to Exhibit 5-10. 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

B

Exhibit 5-10 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 71. Refer to Exhibit 5-10. The expected number of goals per game is a. 0 b. 1 c. 2, since it has the highest probability d. 2.35

D

Exhibit 5-4 Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. 54. Refer to Exhibit 5-4. The probability that the sample contains 2 female voters is a. 0.0778 b. 0.7780 c. 0.5000 d. 0.3456

D

65. Refer to Exhibit 5-8. The appropriate probability distribution for the random variable is a. discrete b. continuous c. either discrete or continuous depending on how the interval is defined d. None of these alternatives is correct.

A

16. 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

B

19. 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

B

Exhibit 5-1 The following represents the probability distribution for the daily demand of computers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 46. Refer to Exhibit 5-1. The expected daily demand is a. 1.0 b. 2.2 c. 2, since it has the highest probability d. of course 4, since it is the largest demand level

B

Exhibit 5-11 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 75. Refer to Exhibit 5-11. The expected number of machine breakdowns per month is a. 2 b. 1.70 c. one, since it has the highest probability d. at least 4

B

Exhibit 5-7 The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. 60. Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is a. .008 b. .096 c. .104 d. .8

B

Exhibit 5-9 The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales (In $1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 69. Refer to Exhibit 5-9. The expected daily sales are a. $55,000 b. $56,000 c. $50,000 d. $70,000

B

43. 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. 0.0600 c. 0.0555 d. 0.2800

C

61. Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is a. .008 b. .096 c. .104 d. .8

C

62. Refer to Exhibit 5-7. The expected number of days Pete will catch fish is a. .6 b. .8 c. 2.4 d. 3

C

68. Refer to Exhibit 5-8. The probability that there are less than 3 occurrences is a. .0659 b. .0948 c. .1016 d. .1239

C

Exhibit 5-2 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. 48. Refer to Exhibit 5-2. 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

C

Exhibit 5-3 Roth 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 51. Refer to Exhibit 5-3. The expected number of new clients per month is a. 6 b. 0 c. 3.05 d. 21

C

77. Refer to Exhibit 5-11. The probability of no breakdowns in a month is a. 0.88 b. 0.00 c. 0.50 d. 0.12

D

80. Refer to Exhibit 5-12. What is the probability that in a given day there will be no accidents? a. 0.00 b. 1.00 c. 0.85 d. 0.15

D

82. Refer to Exhibit 5-13. The standard deviation for the production is a. 4.32 b. 3.74 c. 0.374 d. 0.612

D

Exhibit 5-12 The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Days 0 45 1 75 2 120 3 45 4 15 78. Refer to Exhibit 5-12. What is the probability that in a given day there will be less than 3 accidents? a. 0.2 b. 120 c. 0.5 d. 0.8

D

Exhibit 5-13 Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below. Production Per Month Probability x f(x) 1 0.01 2 0.04 3 0.10 4 0.80 5 0.05 81. Refer to Exhibit 5-13. the expected monthly production level is a. 1.00 b. 4.00 c. 3.00 d. 3.84

D