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The normal distribution is the most important probability ...

Resolved Question:

The normal distribution is the most important probability distribution in the world of statistics. What are the properties of this distribution that make it so powerful and important in statistical analysis?

1. The first reason is directly linked to the mathematical properties of the distribution. If a random sample is taken from a normal distribution, then the distributions of various important functions of the observations can be derived explicitly and will have simple forms. Therefore, it is a mathematical convenience to be able to assume that the distribution from which a random sample is drawn is a normal distribution.

2. The second reason is that many scientist have observed that the random variables obtained from various experiments often can be very well approximated with the normal distribution.

3. The third reason is the central limit theorem. In short it states that if a random sample is taken from some distribution, then even though this distribution is not itself approximately normal, several important functions of the observations in the sample will have a distribution that is approximately normal.

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