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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
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 Originally Posted by markosheehan 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
I guess what they want you to do here is evaluate how much probability mass lies in $[64,80]$ given the underlying distribution, and multiply that by 200.

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 x-mean/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. $p = \Phi\left(\dfrac{80-64}{8}\right)-\Phi\left(\dfrac{64-64}{8}\right)$ $E[\text{# students out of 200 to get a mark }\in [64,80]~] = 200p$

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