Normal Distribution Calculator

Normal Probability Density

x:

σ (Standard Deviation):

μ (Mean):

Probability: -

Formula: f(x) = (1 / (σ√(2π))) * e^(-(1/2)((x-μ)/σ)^2)

This calculates the height of the probability density function at point x.

Normal Cumulative Distribution

Lower:

Upper:

σ (Standard Deviation):

μ (Mean):

Probability: -

This calculates the probability that a random variable falls between the lower and upper bounds.

Use "-Infinity" for the lower bound to calculate P(X ≤ upper).

Inverse Normal

Area (0-1):

σ (Standard Deviation):

μ (Mean):

Φ(z): -

This finds the x-value such that P(X ≤ x) = Area.

Standardising a Normal Distribution

X:

σ (Standard Deviation):

μ (Mean):

z: -

Formula: z = (X - μ) / σ

This converts a value from a normal distribution to its equivalent z-score.