# What is the mathematical difference between the probability density functions of a normal distribution and a standard normal distribution?

##### 1 Answer

Nov 7, 2015

The mean and standard deviation

#### Explanation:

Both are **bell-shaped** and perfectly **symmetrical** about the mean.

Besides that, they are identical with respect to the mathematical properties. For example, the **Empirical Rule** will still hold true regardless if it is a non-Standard Normal distribution. That is, expect about 68% of the distributions to fall within 1 standard deviation of the mean.