My Math Forum Normal approximation and Central Limit Theorem

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 September 23rd, 2015, 09:01 AM #1 Newbie   Joined: Jun 2015 From: OverTheRainbow Posts: 13 Thanks: 0 Normal approximation and Central Limit Theorem Hi, I have the following theorem of Central Limit Theorem: $\displaystyle Z_n = \frac{\bar{X}_n - \mu}{\frac{\sigma}{\sqrt{n}}}$ I know that $\displaystyle \bar{X}_n$ is the mean of all n outcomes of each n trials: $\displaystyle \bar{X}_n = \frac{X_1 + X_2 + ... + X_n}{n}$ I know also that $\displaystyle \mu$ is the mean or expectation of each single trial: $\displaystyle \mu = E(X) = \frac{x_1 + x_2 + ... + x_n}{n}$ I know that sigma is the standard deviation but however, what I don't understand is the denominator in the theorem $\displaystyle \frac{\sigma}{\sqrt{n}}$, what it is? What is that square root of n? thanks!
 September 23rd, 2015, 10:18 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 $\sigma$ is the standard deviation for each individual trial. $\frac{\sigma}{\sqrt{n}}$ is the standard deviation for the average of all n trials.

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