Suppose a single random sample of size n is drawn from any population with mean μ and standard deviation σ. What does the central limit theorem say when n is sufficiently large?

Question

Quizplus · Accepted Answer

The central limit theorem states that when the sample size is sufficiently large, the distribution of the sample mean will be approximately normal, regardless of the distribution of the population. This means that the mean of the sample means will be equal to the population mean, and the standard deviation of the sample means will be equal to the population standard deviation divided by the square root of the sample size. Option A is incorrect as it provides an incorrect formula for the standard deviation of the sample mean. Option B is incorrect as the central limit theorem does not state that the population distribution is exactly normal. Option D is incorrect because although the distribution of the sample mean will approach normality, it will never be exactly normal unless the population distribution is normal.

Suppose a Single Random Sample of Size N Is Drawn