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 if the population is normal, due to the properties of the normal distribution.

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