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Normal Distribution

High School

Definition

The normal (Gaussian) distribution is a continuous probability distribution with a bell-shaped curve symmetric around the mean. It appears widely in nature and society.

Formulas

f(x) = (1)/(σ√2π) e^-((x-μ)²)/(2σ²)

Normal distribution PDF

Z = (X - μ)/(σ)

Standardization (Z-score)

Examples

Example 1

Heights have mean 170cm, SD 10cm. Find P(height > 180cm).

History

Discovered by: Carl Friedrich Gauss (1809)

Gauss discovered the normal distribution while analyzing astronomical measurement errors.

Applications

Quality Control

Six Sigma

Finance

Stock price modeling

Natural Sciences

Measurement error analysis