What is a normal distribution What is a standard normal dist

What is a normal distribution? What is a standard normal distribution? Briefly compare and contrast these two statistical terms.

Solution

A normal distribution is determined by two parameters the mean and the variance.
Now the standard normal distribution is a specific distribution with mean 0 and variance 1. This is the distribution that is used to construct tables of the normal distribution.

Conveniently if X has the a normal distribution with mean m and variance s2 then if we define
Z=Xm / s
Standard Normal Distribution = Z= X- u / sd ~ N(0,1)