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September 10th, 2016, 08:34 AM   #1
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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
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September 10th, 2016, 10:20 AM   #2
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Originally Posted by markosheehan View Post
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?
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September 10th, 2016, 12:24 PM   #3
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i dont really know how to do it but i know it involves the forumla x-mean/standard deviation
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September 10th, 2016, 12:31 PM   #4
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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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