A company has determined that the mean number of days it takes to collect on its accounts receivable is 36, with a standard deviation of 11 days. The company plans to select a random sample of n = 12 accounts and compute the sample mean. Which of the following statements holds true in this situation?
A) The sampling distribution may actually be approximately Normally distributed depending on what the population distribution is.
B) The sampling distribution will always have the same distribution as the population.
C) The sampling variability will be greater than if they had sampled n = 64 accounts.
D) The sampling distribution will certainly be approximately Normally distributed in this case.
E) The sampling distribution cannot be approximately Normally distributed in this case.

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately Normally distributed if the sample size is large enough (n > 30) or if the population from which the sample is taken is Normally distributed. Since we do not know the distribution of the population, we cannot say for certain that the sampling distribution will be Normal. However, it is possible that it could be approximately Normal. Therefore, choice A is the best answer. Choices B, D, and E are all incorrect because they make assumptions about the sampling distribution that may not be true. Choice C is also incorrect because there is no reason to believe that sampling variability would be greater with a smaller sample size.

A Company Has Determined That the Mean Number of Days