A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately
A) normal because is always approximately normally distributed.
B) normal because the sample size is small in comparison to the population size.
C) normal because of the central limit theorem.
D) none of these alternatives is correct.

Question

A sample of 92 observations is taken from an infinite population. The sampling distribution of  is approximately
A) normal because is always approximately normally distributed. 
B) normal because the sample size is small in comparison to the population size. 
C) normal because of the central limit theorem. 
D) none of these alternatives is correct.

Quizplus · Accepted Answer

The central limit theorem states that when taking a random sample from any population with a finite mean and variance, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution, as long as the sample size is large enough (typically n ≥ 30). In this case, n = 92, which is large enough to satisfy the central limit theorem and thus the sampling distribution of the sample mean is approximately normal.

A Sample of 92 Observations Is Taken from an Infinite