I am wondering why so many stats are normally distributed. For example, a typical example is that the heights of people in a university are likely to be normally distributed. One driver of normal distribution is of course the CLT. But the height example seems not connected to the CLT.
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In the example you site it may be a good approximation. Since there are no negative heights it can't be exactly normal. – Michael R. Chernick Apr 27 '17 at 16:59
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1There is probably a duplicate somewhere on this site. – Michael R. Chernick Apr 27 '17 at 17:01
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Actually the height example is related to the CLT. The reason why the normal distribution is so common is because (as per the wikipedia article) 'averages of random variables independently drawn from independent distributions converge in distribution to the normal'
Height has lots of random variables - genetics, diet, pollution, and tons of other effects. It's the concert of all of these small effects that can lead something like height to be normally distributed.
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