How does the Normal Distribution work?

PDF: f(x) = (1/σ√2π) × e^(−(x−μ)²/2σ²) Then: 68-95-99.7 rule: 68% within 1σ, 95.4% within 2σ, 99.7% within 3σ Then: CDF gives P(X ≤ x) — area under the curve to the left of x.

Can you give an example of how to use the Normal Distribution?

Example: Input μ=100, σ=15 (IQ) · x=130 gives a result of z=2.0 · P(IQ<130) = 97.7% · Top 2.3% (130 is 2 standard deviations above mean).

Is the Normal Distribution free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Normal Distribution?

Our Normal Distribution uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Normal Distribution

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The normal (Gaussian) distribution is the most important probability distribution in statistics — bell-shaped, symmetric around the mean. The central limit theorem ensures many real phenomena approach normality with large samples.

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Did You Know?

The normal distribution appears on the old German 10 Deutsche Mark banknote alongside Carl Friedrich Gauss, who developed it while studying measurement errors in astronomy.

References

›Normal distribution — Wikipedia

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