Area of a Normal Distribution

To find P(X≤x) for a normally distributed random variable X with mean μ and standard deviation σ we standardize values from the N(μ,σ) distribution using z=((x-μ)/σ) so that P(X≤x)=P(Z≤z) where Z is a standard normal random variable. Such probabilities are represented as areas to the left of x or z under a corresponding density curve.

This Demonstration provides a visualization of the relationship between a normal distribution N(μ,σ) and the standard normal distribution N(0,1). Specifically, the area to the left of the value x in a N(μ,σ) distribution corresponds to an area to the left of the value's z–score in a standard normal N(0,1) distribution. Likewise, the areas to  the right of x and z correspond to P(X≥x)=P(Z≥z).

THINGS TO TRY

MouseOver ▪ MouseOver ▪ MouseOver ▪ MouseOver

RELATED LINKS

Eric Schulz

© Wolfram Demonstrations Project & Contributors   |   Terms of Use