Galton Board

Bean machine — binomial distribution emerging from random peg bounces

Rows: 8 | σ = √(np(1−p)) = 1.414 | Total balls: 0

Each ball falls through n rows of pegs, bouncing left (p=0.5) or right (q=0.5) at each peg. The final bin position is the sum of n Bernoulli trials — a binomial distribution B(n, 0.5). By the Central Limit Theorem, as n→∞ this converges to a Gaussian N(n/2, n/4). The red curve shows the theoretical normal distribution.