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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 is the standard deviation for each individual trial. is the standard deviation for the average of all n trials. Tags approximation, central, limit, normal, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post bml1105 Probability and Statistics 7 August 21st, 2014 10:24 AM NeedToLearn Advanced Statistics 1 June 21st, 2013 12:26 PM safyras Algebra 0 May 25th, 2011 11:52 AM Mahonroy Advanced Statistics 1 October 11th, 2009 07:32 PM xoxo Advanced Statistics 0 May 22nd, 2009 09:38 PM

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