Statistics MCQs – Sampling Distributions Part 5

81. Suppose it is known that 60% of students at a particular university are smokers. A sample of 500 students from the university is selected at random. What is the approximate probability that at least 280 of these students are smokers?

a. 0.8542

b. 0.6254

c. 0.7236

d. 0.9972

e. 0.9693

Answer: E

82. Exactly 448 pots fit into a potter’s oven. The probability that a pot will crack whilst being baked is 1/8. What is the approximate probability that 70 or more cups will crack?

a. 1.1000

b. 0.5000

c. 0.9732

d. 0.1230

e. 0.0268

Answer: E

83. A recent survey conducted by the traffic department revealed that 80% of motorists in Cape Town have traffic fines outstanding. A retired Statistics professor, now working for the traffic department, selects a random sample of 120 motorists in various areas of Cape Town. What is the approximate probability that more than 96 of the motorists sampled have traffic fines outstanding?

a. 0.4562

b. 0.5438

c. 0.8962

d. 0.8485

e. 0.1515

Answer: A

84. A recent survey conducted by the traffic department revealed that 80% of motorists in Cape Town have traffic fines outstanding. A retired Statistics professor, now working for the traffic department, selects a random sample of 120 motorists in various areas of Cape Town. What is the approximate probability that more than 90 of the motorists sampled have traffic fines outstanding?

a. 0.4562

b. 0.5438

c. 0.8962

d. 0.8485

e. 0.1515

Answer: C

85. A recent survey conducted by the traffic department revealed that 80% of motorists in Cape Town have traffic fines outstanding. A retired Statistics professor, now working for the traffic department, selects a random sample of 120 motorists in various areas of Cape Town. What is the approximate probability that more than 100 of the motorists sampled have traffic fines outstanding?

a. 0.4562

b. 0.5438

c. 0.8962

d. 0.8485

e. 0.1515

Answer: E

86. 60% of university students prefer MCQ tests to written tests. In a random sample of 300 students, what is the probability that more than 55% of them preferred MCQ tests?

a. 0.9616

b. 0.7611

c. 0.0384

d. 0.2389

e. 0.9934

Answer: A

87. 60% of university students prefer MCQ tests to written tests. In a random sample of 300 students, what is the probability that more than 58% of them preferred MCQ tests?

a. 0.9616

b. 0.7611

c. 0.0384

d. 0.2389

e. 0.9934

Answer: B

88. 60% of university students prefer MCQ tests to written tests. In a random sample of 300 students, what is the probability that more than 65% of them preferred MCQ tests?

a. 0.9616

b. 0.7611

c. 0.0384

d. 0.2389

e. 0.9934

Answer: C

89. 60% of university students prefer MCQ tests to written tests. In a random sample of 300 students, what is the probability that more than 62% of them preferred MCQ tests?

a. 0.9616

b. 0.7611

c. 0.0384

d. 0.2389

e. 0.9934

Answer: D

90. 60% of university students prefer MCQ tests to written tests. In a random sample of 300 students, what is the probability that more than 53% of them preferred MCQ tests?

a. 0.9616

b. 0.7611

c. 0.0384

d. 0.2389

e. 0.9934

Answer: E

91. A manufacturer claims that the market share of her product is 60%. What is the probability that in a random sample of 500 customers more than 65% use her product?

a. 0.0113

b. 0.1814

c. 0.9887

d. 0.9147

e. 0.0853

Answer: A

92. A manufacturer claims that the market share of her product is 60%. What is the probability that in a random sample of 500 customers more than 62% use her product?

a. 0.0113

b. 0.1814

c. 0.9887

d. 0.9147

e. 0.0853

Answer: B

93. A manufacturer claims that the market share of her product is 60%. What is the probability that in a random sample of 500 customers more than 55% use her product?

a. 0.0113

b. 0.1814

c. 0.9887

d. 0.9147

e. 0.0853

Answer: C

94. A manufacturer claims that the market share of her product is 60%. What is the probability that in a random sample of 500 customers more than 57% use her product?

a. 0.0113

b. 0.1814

c. 0.9887

d. 0.9147

e. 0.0853

Answer: D

95. A manufacturer claims that the market share of her product is 60%. What is the probability that in a random sample of 500 customers more than 63% use her product?

a. 0.0113

b. 0.1814

c. 0.9887

d. 0.9147

e. 0.0853

Answer: E

96. It is claimed that 15% of all students smoke. What is the probability that in a random sample of 300 students, less than 12% are smokers?

a. 0.072

b. 0.008

c. 0.166

d. 0.834

e. 0.992

Answer: A

97. It is claimed that 15% of all students smoke. What is the probability that in a random sample of 300 students, less than 10% are smokers?

a. 0.072

b. 0.008

c. 0.166

d. 0.834

e. 0.992

Answer: B

98. It is claimed that 15% of all students smoke. What is the probability that in a random sample of 300 students, less than 13% are smokers?

a. 0.072

b. 0.008

c. 0.166

d. 0.834

e. 0.992

Answer: C

99. It is claimed that 15% of all students smoke. What is the probability that in a random sample of 300 students, less than 17% are smokers?

a. 0.072

b. 0.008

c. 0.166

d. 0.834

e. 0.992

Answer: D

100. It is claimed that 15% of all students smoke. What is the probability that in a random sample of 300 students, less than 20% are smokers?

a. 0.072

b. 0.008

c. 0.166

d. 0.834

e. 0.992

Answer: E