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 25cm2. 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 25cm2. 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 25cm2. 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 25cm2. 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