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Because of the Central Limit Theorem, the mean value of sets of observations is distributed Normally. Irrespective of the underlying distribution of a variable, the distribution of a sum (or mean) of such variables tends towards the Normal distribution. So, for sufficiently large samples, all distributions can be approximated by thye Normal distribution.

One of the consequences is that the distribution has been studied extensively and a lot is known about tests based on it.

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Q: Why normal distribution used in solving probability problems?
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