Why we prefer Normal Distribution over the other distributions in Statistics?

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We prefer mostly normal distribution, because most of the data around us follows normal distribution. Example height, weight. Etc will follow normal you can check it by plotting the graph can see the bell curve on the histogram u plotted.
And most importantly by CLT (central limit theorem) and law of large numbers, we can say that as n is large the data follows normal distribution.
The normal distribution is so important due to the Central Limit Theorem. The Central Limit Theorem basically states that as the sample size increases ANY probability distribution can be approximated by the normal distribution and as that sample size increases in size the approximation gets better.




Because it focuses on the mean, or average when stating findings they are always based on averages. For example if you have a body fat test done, they will tell you what your fat content is and then compare it to the average person, based on the normal distribution.




The normal distribution is so important due to the Central Limit Theorem. The Central Limit Theorem basically states that as the sample size increases ANY probability distribution can be approximated by the normal distribution and as that sample size increases in size the approximation gets better. The statement that this works for ANY probability distribution is very powerful, as you can be working with an UNKNOWN probability distribution that you know nothing about, and still you can calculate some decent approximations to it as long as take a large enough sample size.

Because of the Central Limit Theorem: if we average a lot of random variables, which are independent and identically distributed, their average is close to being normally distributed. So, the Normal Distribution is "in touch with nature.":)

The Central Limit theorem states the distribution of an average tends to be Normal, even when the distribution from which the average is computed is isn't.

For example you roll the dice 10 times then take the average, then repeat many times, the distribution of the averages will be approximately Normal.

In simple terms the Normal distribution is useful for study of real world distributions because in the real world a single distribution (like height of men) is a result of other random factors.
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