ch6 problems

108. Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles? a. 0.0000 b. 0.9332 c. 0.0668 d. 0.4993

A

114. Refer to Exhibit 6-10. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course? a. 8.53% b. 18.53% c. 91.47% d. 0.853%

A

50. Given that Z is a standard normal random variable, what is the probability that -2.08 Z 1.46? a. 0.9091 b. 0.4812 c. 0.4279 d. 0.0533

A

53. X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is a. 0.0029 b. 0.0838 c. 0.4971 d. 0.9971

A

54. X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is a. 0.000 b. 0.0055 c. 0.4945 d. 0.9945

A

56. Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5? a. 0.0000 b. 1.0000 c. 0.1915 d. 0.3413

A

58. An exponential probability distribution a. is a continuous distribution b. is a discrete distribution c. can be either continuous or discrete d. must be normally distributed

A

61. Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803? a. -2.06 b. 0.4803 c. 0.0997 d. 3.06

A

64. For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is a. 0.9267 b. 0.4267 c. 1.4267 d. 0.5000

A

70. Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401? a. 1.08 b. 0.1401 c. 2.16 d. -1.08

A

71. Given that Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754? a. 1.16 b. 1.96 c. 2.0 d. 11.6

A

75. Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent? a. 0.0683 b. 0.0213 c. 0.0021 d. 0.1329

A

78. Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is a. zero b. 0.50 c. 0.15 d. 1

A

96. Refer to Exhibit 6-5. The probability that her trip will take exactly 50 minutes is a. zero b. 0.02 c. 0.06 d. 0.20

A

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. 76. Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10? a. 0.25 b. 4.00 c. 5.00 d. zero

A

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. 109. Refer to Exhibit 6-9. What is the probability that a randomly selected computer will have a price of at least $1,530? a. 0.0668 b. 0.5668 c. 0.4332 d. 1.4332

A

107. Refer to Exhibit 6-8. What percentage of tires will have a life of 34,000 to 46,000 miles? a. 38.49% b. 76.98% c. 50% d. 88.49%

B

110. Refer to Exhibit 6-9. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount? a. 62% b. 0.62% c. 0.062% d. 99.38%

B

112. Refer to Exhibit 6-9. If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM? a. 185,500 b. 85,500 c. 513,000 d. not enough information is provided to answer this question

B

115. Refer to Exhibit 6-10. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's? a. 70.39 b. 67.39 c. 50.39 d. 65.39

B

43. The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is a. 0.75 b. 0.5 c. 0.05 d. 1

B

44. Z is a standard normal random variable. The P(-1.96 Z -1.4) equals a. 0.8942 b. 0.0558 c. 0.475 d. 0.4192

B

49. Given that Z is a standard normal random variable, what is the probability that Z -2.12? a. 0.4830 b. 0.9830 c. 0.017 d. 0.966

B

57. Given that Z is a standard normal random variable, what is the value of Z if the are to the left of Z is 0.0559? a. 0.4441 b. 1.59 c. 0.0000 d. 1.50

B

59. Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112? a. 0.3888 b. 1.22 c. 2.22 d. 3.22

B

62. For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is a. 0.4000 b. 0.0146 c. 0.0400 d. 0.5000

B

65. The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old? a. It could be any value, depending on the magnitude of the standard deviation b. 50% c. 21% d. 1.96%

B

66. Z is a standard normal random variable. The P(1.05 < Z < 2.13) equals a. 0.8365 b. 0.1303 c. 0.4834 d. 0.3531

B

69. Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382? a. 1.8 b. 1.54 c. 2.1 d. 1.77

B

72. Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834? a. 0.4834 b. -2.13 c. +2.13 d. zero

B

77. Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is a. zero b. 0.50 c. 0.20 d. 1

B

79. Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is a. 0.25 b. 0.75 c. zero d. 1

B

81. Refer to Exhibit 6-1. The standard deviation of assembly time (in minutes) is approximately a. 1.3333 b. 1.1547 c. 0.1111 d. 0.5773

B

83. Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is a. 0.4772 b. 0.9772 c. 0.0528 d. 0.5000

B

85. Refer to Exhibit 6-2. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. 190

B

90. Refer to Exhibit 6-3. The variance of X is approximately a. 2.309 b. 5.333 c. 32 d. 0.667

B

92. Refer to Exhibit 6-4. The probability that x is between 3 and 6 is a. 0.4512 b. 0.1920 c. 0.2592 d. 0.6065

B

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. 82. Refer to Exhibit 6-2. The probability of a player weighing more than 241.25 pounds is a. 0.4505 b. 0.0495 c. 0.9505 d. 0.9010

B

Exhibit 6-4 f(x) =(1/10) e-x/10 x 0 91. Refer to Exhibit 6-4. The mean of x is a. 0.10 b. 10 c. 100 d. 1,000

B

Exhibit 6-5 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. 94. Refer to Exhibit 6-5. The probability that she will finish her trip in 80 minutes or less is a. 0.02 b. 0.8 c. 0.2 d. 1.00

B

Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. 97. Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000? a. 0.4772 b. 0.9772 c. 0.0228 d. 0.5000

B

Exhibit 6-8 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. 105. Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of at least 30,000 miles? a. 0.4772 b. 0.9772 c. 0.0228 d. 0.5000

B

102. Refer to Exhibit 6-7. What percentage of items will weigh at least 11.7 ounces? a. 46.78% b. 96.78% c. 3.22% d. 53.22%

C

106. Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of at least 47,500 miles? a. 0.4332 b. 0.9332 c. 0.0668 d. 0.4993

C

41. For a standard normal distribution, the probability of z 0 is a. zero b. -0.5 c. 0.5 d. one

C

48. Given that Z is a standard normal random variable, what is the probability that -2.51 Z -1.53? a. 0.4950 b. 0.4370 c. 0.0570 d. 0.9310

C

55. X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is less than 9.7 is a. 0.000 b. 0.4931 c. 0.0069 d. 0.9931

C

68. Z is a standard normal random variable. The P(-1.5 < Z < 1.09) equals a. 0.4322 b. 0.3621 c. 0.7953 d. 0.0711

C

73. Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119? a. 0.381 b. +1.18 c. -1.18 d. 2.36

C

80. Refer to Exhibit 6-1. The expected assembly time (in minutes) is a. 16 b. 2 c. 8 d. 4

C

87. Refer to Exhibit 6-3. The probability that X will take on a value between 21 and 25 is a. 0.125 b. 0.250 c. 0.500 d. 1.000

C

88. Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is a. 0.000 b. 0.125 c. 0.250 d. 1.000

C

93. Refer to Exhibit 6-4. The probability that x is less than 5 is a. 0.6065 b. 0.0606 c. 0.3935 d. 0.9393

C

98. Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500? a. 0.4332 b. 0.9332 c. 0.0668 d. 0.5000

C

Exhibit 6-10 A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. 113. Refer to Exhibit 6-10. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? a. 90.51 b. 93.2 c. 88.51 d. 100.00

C

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. 86. Refer to Exhibit 6-3. The probability density function has what value in the interval between 20 and 28? a. 0 b. 0.050 c. 0.125 d. 1.000

C

Exhibit 6-7 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. 100. Refer to Exhibit 6-7. What is the probability that a randomly selected item will weigh more than 10 ounces? a. 0.3413 b. 0.8413 c. 0.1587 d. 0.5000

C

101. Refer to Exhibit 6-7. What is the probability that a randomly selected item will weigh between 11 and 12 ounces? a. 0.4772 b. 0.4332 c. 0.9104 d. 0.0440

D

103. Refer to Exhibit 6-7. What percentage of items will weigh between 6.4 and 8.9 ounces? a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

D

104. Refer to Exhibit 6-7. What is the probability that a randomly selected item weighs exactly 8 ounces? a. 0.5 b. 1.0 c. 0.3413 d. 0.0000

D

111. Refer to Exhibit 6-9. What is the minimum value of the middle 95% of computer prices? a. $1,768.80 b. $1,295.80 c. $2,400.00 d. $768.80

D

25. The probability density function for a uniform distribution ranging between 2 and 6 is a. 4 b. undefined c. any positive value d. 0.25

D

31. Consider a binomial probability experiment with n = 3 and p = 0.1. Then, the probability of x = 0 is a. 0.0000 b. 0.0001 c. 0.001 d. 0.729

D

39. A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is a. zero b. (a - b) c. (b - a) d. 1/(b - a)

D

46. Z is a standard normal random variable. The P (1.20 Z 1.85) equals a. 0.4678 b. 0.3849 c. 0.8527 d. 0.0829

D

47. Z is a standard normal random variable. The P (-1.20 Z 1.50) equals a. 0.0483 b. 0.3849 c. 0.4332 d. 0.8181

D

51. Z is a standard normal random variable. The P (1.41 < Z < 2.85) equals a. 0.4978 b. 0.4207 c. 0.9185 d. 0.0771

D

52. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is a. 0.0222 b. 0.4190 c. 0.5222 d. 0.9190

D

60. Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754? a. 0.377 b. 0.123 c. 2.16 d. 1.16

D

63. For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is a. 0.1600 b. 0.0160 c. 0.0016 d. 0.9452

D

67. Z is a standard normal random variable. The P(Z > 2.11) equals a. 0.4821 b. 0.9821 c. 0.5 d. 0.0174

D

74. Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901? a. 1.96 b. -1.96 c. 0.4505 d. 1.65

D

84. Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds? a. 28.81% b. 0.5762% c. 0.281% d. 57.62%

D

89. Refer to Exhibit 6-3. The mean of X is a. 0.000 b. 0.125 c. 23 d. 24

D

95. Refer to Exhibit 6-5. The probability that her trip will take longer than 60 minutes is a. 1.00 b. 0.40 c. 0.02 d. 0.600

D

99. Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000? a. 38.49% b. 38.59% c. 50% d. 76.98%

D