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

According to the central limit theorem, if the sample size is large enough (typically n≥30), then the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution. Therefore, the answer is C.

A Sample of 92 Observations Is Taken from an Infinite