---
tag: 05AQE0QR0D
kind: concept
name: Normal distribution
aliases: [gaussian-distribution, gaussian, bell-curve]
msc: ["60E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Normal_distribution
    locator: lead section
same_as:
  wikidata: Q133871
  wikipedia: Normal distribution
---

## Summary

The normal distribution with mean $\mu$ and variance $\sigma^2$ is the continuous distribution on $\mathbb{R}$ with the bell-shaped density $\frac{1}{\sqrt{2\pi\sigma^2}} e^{-(x-\mu)^2/(2\sigma^2)}$.
By the central limit theorem, it is the approximate law of a sum of many small independent effects. The node [[normal distribution|07RXBVTVZB]] gives the precise definition.