The normal distribution describes how many natural phenomena cluster around a mean, tapering off symmetrically on both sides. It emerges whenever many small, independent random effects add together — a consequence of the Central Limit Theorem.

Key insight 68% of values fall within ±1σ, 95% within ±2σ, 99.7% within ±3σ.

Real-world examples

Heights of people Measurement errors IQ scores Blood pressure readings