The normal distribution has occupied a very important role in statistics. We enumerate below some of its important applications.
Normal Distribution in Statistics, Data Science, and Parametric Statistics:
- The probability of standard normal variate going outside the limits ±3 is practically zero. In other words, in all probability, we should expect a standard normal variate to lie between the limits ±3. This property of the normal distribution forms the basis of the large sample theory in the theory of sampling.
- Most of the discrete probability distributions (e.g., Binomial distribution, Poisson distribution) tend to normal distribution as n, the number of trials increases. For large values of n, computation of probability for discrete distributions becomes quite tedious and time-consuming. In such cases, the normal approximation can be used with great ease and convenience.
- Almost all the exact sampling distributions, e.g., Student’s t-distribution, Snedecor’s F-distribution, Fisher’s Z-distribution and Chi square distribution conform to normal distribution for large degrees of freedom.
- The whole theory of exact sample (small sample) tests, that is the T-test, F test, Chi-square tests, etc., is based on the fundamental assumption that the parent population from which the samples have been drawn follows the normal distribution.
- Perhaps, one of the most important applications of the Normal distribution is in one of the most fundamental theorems in the theory of Statistics, that is, the Central Limit Theorem.
Normal Distribution In Business and Decision Making:
- The normal distribution is used in Statistical Quality Control in Industry for the setting of control limits for the construction of control charts.
- The normal distribution is used in the testing of hypotheses which allows us to make business decisions.
- The regression analysis is based on the fact that the errors are normally distributed. The method of regression allows us to make predictions about the future on the basis of past data. These predictions are helpful in making business decisions and economic forecasts.
- The methods based on normal distributions are used in the healthcare industry to accept or reject results of clinical trials.
- It is an experimental fact that measurement errors are distributed according to the laws of the normal distribution. Thus the normal distribution is the basis behind the law of errors.