# Statistics MCQs – Continuous Distributions Part 7

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121. The diameters of oranges found in the orchard of an orange farm follow a normal distribution with a mean of 120mm and a standard deviation of 10mm. What proportion of oranges in the orchard have a diameter between 100mm and 115mm?

a. 0.6826

b. 0.8186

c. 0.3829

d. 0.4332

e. 0.2858

Answer: E

122. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is within one standard deviation of the mean?

a. 0.683

b. 0.954

c. 0.271

d. 0.340

e. 0.161

Answer: A

123. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50 and 90?

a. 0.683

b. 0.954

c. 0.271

d. 0.340

e. 0.161

Answer: B

124. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 65 and 72?

a. 0.683

b. 0.954

c. 0.271

d. 0.340

e. 0.161

Answer: C

125. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84?

a. 0.683

b. 0.954

c. 0.271

d. 0.340

e. 0.161

Answer: D

126. The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 50 and 61?

a. 0.683

b. 0.954

c. 0.271

d. 0.340

e. 0.161

Answer: E

127. The starting annual salaries of newly qualified chartered accountants (CA՚s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R160,000 and R190,000 per annum?

a. 0.819

b. 0.242

c. 0.286

d. 0.533

e. 0.307

Answer: A

128. The starting annual salaries of newly qualified chartered accountants (CA՚s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R165,000 and R175,000 per annum?

a. 0.819

b. 0.242

c. 0.286

d. 0.533

e. 0.307

Answer: B

129. The starting annual salaries of newly qualified chartered accountants (CA՚s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R185,000 and R200,000 per annum?

a. 0.819

b. 0.242

c. 0.286

d. 0.533

e. 0.307

Answer: C

130. The starting annual salaries of newly qualified chartered accountants (CA՚s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R170,000 and R185,000 per annum?

a. 0.819

b. 0.242

c. 0.286

d. 0.533

e. 0.307

Answer: D

131. The starting annual salaries of newly qualified chartered accountants (CA՚s) in South Africa follow a normal distribution with a mean of R180,000 and a standard deviation of R10,000. What is the probability that a randomly selected newly qualified CA will earn between R150,000 and R175,000 per annum?

a. 0.819

b. 0.242

c. 0.286

d. 0.533

e. 0.307

Answer: E

132. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p (85 < X < 90) ?

a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533

Answer: A

133. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p (70 < X < 80) ?

a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533

Answer: B

134. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p (60 < X < 75) ?

a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533

Answer: C

135. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p (75 < X < 95) ?

a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533

Answer: D

136. Given that X is Normally distributed with a mean of 80 and a variance of 100, what is p (70 < X < 85) ?

a. 0.150

b. 0.341

c. 0.286

d. 0.625

e. 0.533

Answer: E

137. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm^{2}. What proportion of students are between 162cm and 182cm in height?

a. 0.954

b. 0.601

c. 0.718

d. 0.883

e. 0.270

Answer: A

138. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm^{2}. What proportion of students are between 170cm and 180cm in height?

a. 0.954

b. 0.601

c. 0.718

d. 0.883

e. 0.270

Answer: B

139. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm^{2}. What proportion of students are between 160cm and 175cm in height?

a. 0.954

b. 0.601

c. 0.718

d. 0.883

e. 0.270

Answer: C

140. In a large statistics class the heights of the students are normally distributed with a mean of 172cm and a variance of 25cm^{2}. What proportion of students are between 165cm and 181cm in height?

a. 0.954

b. 0.601

c. 0.718

d. 0.883

e. 0.270

Answer: D