To find

for a normally distributed random variable

with mean

and standard deviation

we standardize values from the

distribution using

so that

where

is a standard normal random variable. Such probabilities are represented as areas to the left of

or

under a corresponding density curve.

This Demonstration provides a visualization of the relationship between a normal distribution

and the standard normal distribution

. Specifically, the area to the left of the value

in a

distribution corresponds to an area to the left of the value's

–score in a standard normal

distribution. Likewise, the areas to the right of

and

correspond to

.