If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean $\bar { X }$ will be:
A)normal for all values of n.
B)normal only for n 30.
C)approximately normal for all values of n.
D)approximately normal only for n 30.

Question

If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean $\bar { X }$ will be:
A)normal for all values of n.
B)normal only for n > 30.
C)approximately normal for all values of n.
D)approximately normal only for n > 30.

Quizplus · Accepted Answer

The sampling distribution of the sample mean $\bar { X }$ is normal for all values of n when the population from which the sample is drawn is normal, according to the Central Limit Theorem. This holds true regardless of the sample size n.

If a Random Sample of Size N Is Drawn from a Normal