StatisticsAdvanced12 min read • October 4, 2025

The Normal Distribution: Nature’s Most Common Curve

From heights to test scores, this curve shows up everywhere.

The Function (for the curious)

f(x) = (1/(σ√(2π))) · e^{-(1/2)((x-μ)/σ)^2}

Intuition First

  • μ (mu) is the center—average value
  • σ (sigma) is the spread—how varied the data are
  • About 68% of data fall within 1σ, 95% within 2σ

Practical Example

Test scores are normally distributed with μ = 75 and σ = 10. A score of 85 is 1σ above average (z = 1). That puts you around the 84th percentile.

Try This

Convert three numbers from your life to z-scores—height, commute time, exam score—and compare.

Practice with Probability Tools →