ASQ Certified Quality Engineer (CQE) — Question 7

Periodically, a sample of 20 items are randomly selected from a population that is normally distributed, the average is computed, and plotted. Which of the following statements is correct?
I. The average of the logarithms of the values is lognormally distributed.
II. The standard deviation of the averages is equal to the standard deviation of the individuals divided by the square root of 20.
III. The variance of the averages is equal to the variance of the individuals divided by the square root of 20.

Answer options

• A. I only
• B. II only
• C. I and II only
• D. I and III only B

Correct answer:

Explanation

Statement II is correct because the standard deviation of the sample averages is indeed the standard deviation of the population divided by the square root of the sample size (20). Statement I is incorrect because the average of the logarithms does not imply a lognormal distribution, and statement III is also incorrect since the variance of averages is the variance of individuals divided by the sample size, not the square root.