How to Calculate Normal Distribution
What is Normal Distribution?
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.
Step-by-Step Guide
- 1PDF: f(x) = (1/σ√2π) × e^(−(x−μ)²/2σ²)
- 268-95-99.7 rule: 68% within 1σ, 95.4% within 2σ, 99.7% within 3σ
- 3CDF gives P(X ≤ x) — area under the curve to the left of x
Worked Examples
Input
μ=100, σ=15 (IQ) · x=130
Result
z=2.0 · P(IQ<130) = 97.7% · Top 2.3%
130 is 2 standard deviations above mean
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