# Area of a Normal Distribution

Area of a Normal Distribution

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 .

P(X≤x)

X

μ

σ

N(μ,σ)

z=

x-μ

σ

P(X≤x)=P(Z≤z)

Z

x

z

N(μ,σ)

N(0,1)

x

N(μ,σ)

z

N(0,1)

x

z

P(X≥x)=P(Z≥z)