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Normal Distribution

Statistical properties

mean | μ
mode | μ
standard deviation | σ
variance | σ^2
skewness | 0

Probability density function (PDF)

e^(-(x - μ)^2/(2 σ^2))/(sqrt(2 π) σ)

Plots of PDF for typical parameters

Plots of PDF for typical parameters

Cumulative distribution function (CDF)

P (X<=x) = 1/2 erfc((μ - x)/(sqrt(2) σ))

Plots of CDF for typical parameters

Plots of CDF for typical parameters

Percentiles

10th | μ - 1.28155 σ
25th | μ - 0.67449 σ
50th | μ
75th | μ + 0.67449 σ
90th | μ + 1.28155 σ

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