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
.
