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) There is no way to determine what the mean of the sampling distribution is without knowing the specific shape of the population.
B) The sampling distribution will have the same distribution as the population, provided that the population is not normally distributed.
C) The sampling error will be larger than if they had sampled n = 64 accounts.
D) The sampling distribution may actually be approximately normally distributed depending on what the population distribution is.

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size of n = 12 is large enough to invoke the central limit theorem.

A Company Has Determined That the Mean Number of Days