Statistics

Normal Distribution

Bell curve and 68-95-99.7 rule

  • High school
  • about 4 min
  • 3 of 4 in the family
Not started
-4-3-2-101234μ=0P(μ±1σ) ≈ 68.3%
μ = 0
σ = 1.0
Shaded σ
f(x)=1σ2πe−12(x−μσ)2f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Normal distribution: 68% of data lies within 1σ, 95% within 2σ, 99.7% within 3σ (empirical rule). Shape depends on μ (center) and σ (width).