LaTeX
f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}Variables
- μ: mean
- σ: positive standard deviation
How to use this formula
Defines the bell-shaped normal probability density.
Important notes
- Probabilities are areas under the density curve.
Quick example
The density is symmetric around μ.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Probabilities are areas under the density curve.
- For the Normal Distribution Density, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For a real-valued result, each even-root radicand must be nonnegative unless complex values are intended.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
The density is symmetric around μ.
Common mistakes
- When copying Normal Distribution Density, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not assume events are independent or mutually exclusive unless the problem states or proves that condition.
Continue the workflow
Use Normal Distribution Density in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Normal Distribution Density used for?
Defines the bell-shaped normal probability density.
Can I copy this formula as LaTeX?
Yes. Copy f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.