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today my teacher asked why do we need the other continuous distributions if everything is just converging to normal distributions when n is greater or equal to 30. I may partly understand the question but I want to understand it well.

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    $\begingroup$ "everything is just converging to normal distributions when n is greater or equal to 30" Here's a hint: it is not the case that everything converges to normal distributions when n is at least 30. Have a try at restating this more precisely. What is it that converges to the normal distribution? $\endgroup$ – jkpate Dec 15 '20 at 17:07
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    $\begingroup$ Why do we need numbers when everything just converges to zero? ;-) $\endgroup$ – whuber Dec 15 '20 at 17:55
  • $\begingroup$ Please add the self-study tag & read its wiki. $\endgroup$ – kjetil b halvorsen Dec 15 '20 at 18:01
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Assuming you're referring to Central Limit Theorem, note that it has conditions as well (i.e. finite mean and variance). For example, sum/mean of Cauchy distributed RVs doesn't converge to normal distribution.

Also, the following question that's posed by your teacher needs context. Other distributions have very well use cases, too.

why do we need the other continuous distributions

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Your teacher appears to be alluding a common misinterpretation of the central limit theorem.

The central limit theorem concerns the convergence of $ \dfrac{\bar{X} - \mu}{\sigma/\sqrt{n}} $, not of the data themselves.

Under mild conditions that are likely to be met in an introductory statistics class, as the sample size $n$ gets large (maybe $30$ is enough, maybe you need $30$ trillion bazillion), the sample distribution converges to the population distribution. This is the Glivenko–Cantelli theorem.

In other words, by Glivenko–Cantelli, as we get a larger and larger sample size, we get a better and better representation of the population.

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  • $\begingroup$ Your teacher also mentioned about continuous distributions, but the central limit theorem applies to discrete distributions, too! $\endgroup$ – Dave Dec 15 '20 at 17:28

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