Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for
A)only large sample sizes
B)only small sample sizes
C)any sample size
D)only samples of size thirty or greater

Question

Whenever the population has a normal probability distribution, the sampling distribution of  is a normal probability distribution for
A)only large sample sizes 
B)only small sample sizes 
C)any sample size 
D)only samples of size thirty or greater

Quizplus · Accepted Answer

The Central Limit Theorem states that for any population with a finite mean and standard deviation, the sampling distribution of the mean for sample sizes of n will approach a normal distribution as n approaches infinity, regardless of the population distribution. Therefore, the sampling distribution of the mean is normal for any sample size, provided the population itself is normally distributed or sufficiently large enough to invoke the Central Limit Theorem.

Whenever the Population Has a Normal Probability Distribution, the Sampling