# Math Help - Central Limit Theorem: Approximating Sample Mean

1. ## Central Limit Theorem: Approximating Sample Mean

Hi,

I'm having trouble with this problem:
http://users.encs.concordia.ca/~b_zgeb/problem10.png

This is my work so far:
http://users.encs.concordia.ca/~b_zg...m10-answer.png

The problem is the $\theta(30)$. 30 seems like a ridiculous value for normal distribution and I have a feeling it's supposed to be 3. Any thoughts?

Bronson

2. Your answer is correct. As the s.d. of the mean is divided by the sqrt of sample size, for a sample of n=100, the sample mean is going to have a relatively small standard deviation. A large sample size "dilutes" the variance of the mean making it unlikely that you will have much variance from sample to sample.

3. Thanks! I appreciate your help.