Question

The Standard Normal Distribution is going to be a major focus focus through much of the remainder of this course. Why do you think we will focus so much on this distribution (as opposed to the Uniform, Binomial, Poisson, and other distributions). Consider the "real world" when thinking about your response.

Answer 1

The normal distribution is a good approximation in many cases. Certain discrete distributions such as Poisson and binomial can be approximated by the normal distribution, especially when the sample size is large.

When we are dealing with a large population, the distribution of the mean from any of the smaller samples from the population follows a normal distribution. This is the essence of the Central Limit Theorem and is one of the main reasons for the popularity of normal distribution.

Many of the data we encounter in real life also follow normal distributions. Take, for example, the marks in a class or the heights and weights of a set of people.

Many statistical tests assume that the data follows a normal distribution. Most of these are only possible because of the properties of normal distribution.