# Statistics MCQs – Sampling Distributions Part 4

Dr. Manishika Jain- Join online Paper 1 intensive course. Includes tests and expected questions.

61. It is believed that 70 % of first-year statistics students got A՚s for their final matric exams. If 100 first-year statistics students are randomly selected, what is the approximate probability that more than 81 of them got A՚s for matric?

a. 0.0110

b. 0.0060

c. 0.4562

d. 0.1151

e. 0.9808

Answer: B

62. It is believed that 70 % of first-year statistics students got A՚s for their final matric exams. If 100 first-year statistics students are randomly selected, what is the approximate probability that more than 70 of them got A՚s for matric?

a. 0.0110

b. 0.0060

c. 0.4562

d. 0.1151

e. 0.9808

Answer: C

63. It is believed that 70 % of first-year statistics students got A՚s for their final matric exams. If 100 first-year statistics students are randomly selected, what is the approximate probability that more than 75 of them got A՚s for matric?

a. 0.0110

b. 0.0060

c. 0.4562

d. 0.1151

e. 0.9808

Answer: D

64. It is believed that 70 % of first-year statistics students got A՚s for their final matric exams. If 100 first-year statistics students are randomly selected, what is the approximate probability that more than 60 of them got A՚s for matric?

a. 0.0110

b. 0.0060

c. 0.4562

d. 0.1151

e. 0.9808

Answer: E

65. The probability of suffering a miscarriage during the first trimester (three months) of pregnancy is believed to be 0.2 If 100 woman are observed during the first trimester of their pregnancies, what is the approximate probability that at most 20 of them will suffer a miscarriage?

a. 0.5517

b. 0.7357

c. 0.1292

d. 0.0087

e. 0.3520

Answer: A

66. The probability of suffering a miscarriage during the first trimester (three months) of pregnancy is believed to be 0.2 If 100 woman are observed during the first trimester of their pregnancies, what is the approximate probability that at most 22 of them will suffer a miscarriage?

a. 0.5517

b. 0.7357

c. 0.1292

d. 0.0087

e. 0.3520

Answer: B

67. The probability of suffering a miscarriage during the first trimester (three months) of pregnancy is believed to be 0.2 If 100 woman are observed during the first trimester of their pregnancies, what is the approximate probability that at most 15 of them will suffer a miscarriage?

a. 0.5517

b. 0.7357

c. 0.1292

d. 0.0087

e. 0.3520

Answer: C

68. The probability of suffering a miscarriage during the first trimester (three months) of pregnancy is believed to be 0.2 If 100 woman are observed during the first trimester of their pregnancies, what is the approximate probability that at most 10 of them will suffer a miscarriage?

a. 0.5517

b. 0.7357

c. 0.1292

d. 0.0087

e. 0.3520

Answer: D

69. The probability of suffering a miscarriage during the first trimester (three months) of pregnancy is believed to be 0.2 If 100 woman are observed during the first trimester of their pregnancies, what is the approximate probability that at most 18 of them will suffer a miscarriage?

a. 0.5517

b. 0.7357

c. 0.1292

d. 0.0087

e. 0.3520

Answer: E

70. It is known that, if an apple is stung by a certain kind of insect while still hanging on the apple tree, there is a 35 % chance that the apple will be infested by worms. If 50 apples that have all been stung are picked from a tree, what is the approximate probability that at least 25 of them are infested by worms?

a. 0.0188

b. 0.8133

c. 0.2776

d. 0.9911

e. 0.1170

Answer: A

71. It is known that, if an apple is stung by a certain kind of insect while still hanging on the apple tree, there is a 35 % chance that the apple will be infested by worms. If 50 apples that have all been stung are picked from a tree, what is the approximate probability that at least 15 of them are infested by worms?

a. 0.0188

b. 0.8133

c. 0.2776

d. 0.9911

e. 0.1170

Answer: B

72. It is known that, if an apple is stung by a certain kind of insect while still hanging on the apple tree, there is a 35 % chance that the apple will be infested by worms. If 50 apples that have all been stung are picked from a tree, what is the approximate probability that at least 20 of them are infested by worms?

a. 0.0188

b. 0.8133

c. 0.2776

d. 0.9911

e. 0.1170

Answer: C

73. It is known that, if an apple is stung by a certain kind of insect while still hanging on the apple tree, there is a 35 % chance that the apple will be infested by worms. If 50 apples that have all been stung are picked from a tree, what is the approximate probability that at least 10 of them are infested by worms?

a. 0.0188

b. 0.8133

c. 0.2776

d. 0.9911

e. 0.1170

Answer: D

74. It is known that, if an apple is stung by a certain kind of insect while still hanging on the apple tree, there is a 35 % chance that the apple will be infested by worms. If 50 apples that have all been stung are picked from a tree, what is the approximate probability that at least 22 of them are infested by worms?

a. 0.0188

b. 0.8133

c. 0.2776

d. 0.9911

e. 0.1170

Answer: E

75. One fifth of a given population has a minor eye defect. A sample of 100 people from the given population is selected at random. Approximate the probability that more than 20 of these people have a minor eye defect.

a. 0.45

b. 0.50

c. 0.20

d. 0.80

e. 0.72

Answer: A

76. A car ferry can accommodate 298 cars. Because bookings are not always taken up, the operators accept 335 bookings for each ferry crossing, hoping that no more than 298 cars arrive. If individual bookings are taken up independently with probability 0.85, what is the approximate probability that more cars will arrive than can be accommodated on the ferry?

a. 0.0179

b. 0.0080

c. 0.1894

d. 0.0505

e. 0.0033

Answer: A

77. A car ferry can accommodate 300 cars. Because bookings are not always taken up, the operators accept 335 bookings for each ferry crossing, hoping that no more than 300 cars arrive. If individual bookings are taken up independently with probability 0.85, what is the approximate probability that more cars will arrive than can be accommodated on the ferry?

a. 0.0179

b. 0.0080

c. 0.1894

d. 0.0505

e. 0.0033

Answer: B

78. A car ferry can accommodate 290 cars. Because bookings are not always taken up, the operators accept 335 bookings for each ferry crossing, hoping that no more than 290 cars arrive. If individual bookings are taken up independently with probability 0.85, what is the approximate probability that more cars will arrive than can be accommodated on the ferry?

a. 0.0179

b. 0.0080

c. 0.1894

d. 0.0505

e. 0.0033

Answer: C

79. A car ferry can accommodate 295 cars. Because bookings are not always taken up, the operators accept 335 bookings for each ferry crossing, hoping that no more than 295 cars arrive. If individual bookings are taken up independently with probability 0.85, what is the approximate probability that more cars will arrive than can be accommodated on the ferry?

a. 0.0179

b. 0.0080

c. 0.1894

d. 0.0505

e. 0.0033

Answer: D

80. A car ferry can accommodate 302 cars. Because bookings are not always taken up, the operators accept 335 bookings for each ferry crossing, hoping that no more than 302 cars arrive. If individual bookings are taken up independently with probability 0.85, what is the approximate probability that more cars will arrive than can be accommodated on the ferry?

a. 0.0179

b. 0.0080

c. 0.1894

d. 0.0505

e. 0.0033

Answer: E