Area of a Normal Distribution
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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
.
Contributed by: Eric Schulz (April 2007)
Open content licensed under CC BY-NC-SA
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"Area of a Normal Distribution"
http://demonstrations.wolfram.com/AreaOfANormalDistribution/
Wolfram Demonstrations Project
Published: April 27 2007