This is called the Normal variable with parameters,

For any such transformation we have:
if
,
then
the density of *Y* is

The two parameters that are needed to define a normal are: , , this explanation will be developed in chapter 6.

In general if you have a Normal random variable with parameters
and ,
we need to standardize it, because
the probabilities cannot be computed from a closed form
formula,
this is done by standardizing, say

Now is a standard variable so we can use the distribution function

A web site that allows you to look up some probabilities for Normal distributions: