Mathematical Methods · normal distribution · manipulative

μ slides the bell; σ stretches it

On fixed axes, change μ and σ — the curve moves and widens, but the total area under the density stays 1.

f(x) μ σ bands

Vertical scale locked so narrowing (small σ) is real height growth, not zoom

Parameters

0
1
Shade ±1σ
empirical rule ≈ 68%
Shade ±2σ
empirical rule ≈ 95%
Shade ±3σ
empirical rule ≈ 99.7%

Working