Probability

Normal Distribution Formula - Probability

Learn the normal distribution formula with examples, step-by-step guide, and calculator tools. Calculate probability density for normal distribution

The normal distribution formula is a fundamental concept in probability. Calculate probability density for normal distribution. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}\]

Variables

f(x)
Probability density
x
Value
μ
Mean
σ
Standard deviation

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [0,1] → Standard normal: μ=0, σ=1

Example 2

Example 2: 0.399 at x=0

Frequently Asked Questions

What is the normal distribution formula?

Calculate probability density for normal distribution

How do I calculate normal distribution formula?

Use the formula: f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}. Follow the steps provided above.

What tools can help with normal distribution formula?

We provide online calculators: normal-distribution-calculator

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