Whenever the sampled population has a normal distribution,the sampling distribution of $\bar { x }$Is normal:
A)for only large sample sizes.
B)for only small sample sizes.
C)for any sample size.
D)for only samples of exactly 30.
E)for only samples of sizes greater than 31.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean $\bar{x}$ is normal for any sample size when the population from which samples are drawn is normally distributed. This is a result of the Central Limit Theorem, which also states that if the population is not normal, the sampling distribution of the sample mean will approximate a normal distribution as the sample size becomes large (usually n > 30). However, if the population is already normal, the sample size does not matter for the sampling distribution of the mean to be normal.

Whenever the Sampled Population Has a Normal Distribution,the Sampling Distribution xˉ\bar { x }xˉ

Whenever the Sampled Population Has a Normal Distribution,the Sampling Distribution $\bar { x }$