Importance of Normal Distribution

The normal distribution as great significance in statistical work because of the following reasons.

1. The Normal Distribution has the remarkable place stated in the central limit theorem, most imporant of which is the sample mean and sample variance tends to be normally distributed as the sample size becomes large.
2. Even if a variable is not Normal Distributed, it can sometimes be brought to normal form by sample transformation of the variable.
3. Many of the sampling ditributions like student t, F, etc also tend to Normal Distribution.
4. The sampling distribution and testa of hypothesis are based upon the assumption that samples have been drawn from a Normal population with mean μ and variance ^2.
5. Normal Distribution find large application in statistical quality control
6. As n becomes large, the Normal Distribution serves as a good appreciation for many descrete distributions (Binomial, Poisson)
7. In theoretical statistics, many problems can be solved only under the assumption of a Normal Distribution.
8. The Normal Distribution has numerous mathematical propertied which make it popular and esay to manipulate.