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September 10th, 2016, 08:34 AM  #1 
Member Joined: May 2016 From: Ireland Posts: 96 Thanks: 1  Statistics
The mark X of an exam is normally distributed with a mean of 64 and a standard deviation of 8. If 200 students sit the exam how many students would you expect to obtain a mark between 64 and 80

September 10th, 2016, 10:20 AM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,311 Thanks: 1223  Quote:
Do you know how to do that?  
September 10th, 2016, 12:24 PM  #3 
Member Joined: May 2016 From: Ireland Posts: 96 Thanks: 1 
i dont really know how to do it but i know it involves the forumla xmean/standard deviation

September 10th, 2016, 12:31 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,311 Thanks: 1223 
let $\Phi(x) = \displaystyle{\int_{\infty}^x}\dfrac {1}{\sqrt{2\pi}\sigma}e^{\frac{t^2}{\sigma^2}}~dt$ I.e. it's the CDF of the standard Normal distribution. $p = \Phi\left(\dfrac{8064}{8}\right)\Phi\left(\dfrac{6464}{8}\right)$ $E[\text{# students out of 200 to get a mark }\in [64,80]~] = 200p$ 

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