The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes and are large.

Question

The sampling distribution of  is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes  and  are large.

Quizplus · Accepted Answer

This statement is true according to the central limit theorem, which states that for large sample sizes, the sampling distribution of means will be approximately normal regardless of the underlying distribution of the population. For smaller sample sizes, the distribution of the population does have an effect on the sampling distribution.

The Sampling Distribution of Is Normal If the Sampled