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Suppose you have a random variable, X, with any distribution. Suppose you take a sample of n independent observations, X1, X2, ... Xn and calculate their mean. Repeat this process several times. Then as the sample size increases and the number of repeats increases, the distribution of the means tends towards a normal distribution. This is due to the Central Limit Theorem.

One consequence is that many common statistical measures have an approximately normal distribution.

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Q: Why is the normal probability distribution widely used in practice?
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