Distribution Question

[danville82]

Hello everyone,

I have been stressing over this problem for a few days now. Can anyone help me out?

The amount of time a stockbroker spends with a new client has a mean
45 minutes and standard deviation 12 minutes. The distribution of times is not normal.

Suppose a sample of 8 new client meetings is selected.
What can you say about the sampling distribution of the
sample mean?

Suppose a sample of 36 new client meetings is selected.
What is the probability that the sample mean is at most 50
minutes?

Explain why it is possible to determine the probability in
part (b).
What theorem allows you to do so?

 

[tkhunny]

Why are you stressing? Varince of a Sample Mean decreases as the sample size increases. \(\displaystyle \frac{12}{\sqrt{8}}\) comes to mind as a good possibility if it were normal. It does approach Normal in the limit. This would make it more Normal than the original distribution.

Law of Large Numbers?