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)