The central limit theorem states that if the population is normally distributed, then the .
A) mean of the population can be calculated without using samples
B) standard error of the mean will not vary from the population mean
C) sampling distribution of the mean will vary from sample to sample
D) sampling distribution of the mean will also be normal for any sample size

Question

Quizplus · Accepted Answer

According to the central limit theorem, if the population is normally distributed, the sampling distribution of the mean will also be normal for any sample size. This means that as sample size increases, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution. Option A is incorrect because the central limit theorem refers to the behavior of the sampling distribution, not the population mean. Option B is incorrect because the standard error of the mean will vary from the population mean. Option C is partially correct, but the key point of the central limit theorem is that the sampling distribution will be normal, not that it will vary from sample to sample.

The Central Limit Theorem States That If the Population Is