# A normally distributed population has a mean of 40 and a standard deviation of 12. What does the Central Limit Theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?

Mar 27, 2018

see below

#### Explanation:

If X is the random variable for the Normal distribution then

X~N(40,12^2)

for sample sizes of 100 the sampling distribution of the mean follows the following distribution, according to the Central Limit Theorem

barX~N(40,12^2/100)

the Central Limit theorem is useful because it doesn't matter what the, background distribution is providing the sample size, $n \ge 30$ the distribution of the sample mean will follow approximately a Normal distribution

barX~N(mu,sigma^2/n)