For a given population with a normal probability distribution, the sampling distribution of is a normal probability distribution for:
A) small sample sizes only.
B) any sample size.
C) large sample sizes only.
D) sample sizes greater than 30 only.

Question

For a given population with a normal probability distribution, the sampling distribution of  is a normal probability distribution for:
A) small sample sizes only. 
B) any sample size. 
C) large sample sizes only. 
D) sample sizes greater than 30 only.

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of means will be approximately normally distributed regardless of the size of the sample as long as the sample is taken from a population that has a normal distribution or a sample size larger than 30. Therefore, the sampling distribution of means will be a normal probability distribution for any sample size if the population has a normal probability distribution.

For a Given Population with a Normal Probability Distribution, the Sampling