If everything is random, why does it always become bell-shaped?
For each bead, it is completely random whether it bounces left or right at each peg. But when you drop hundreds of beads, the shape they form at the bottom becomes the same bell shape, bulging in the middle, every time. This is why the normal distribution appears so often in the world around us.
How it works: Which bin a bead reaches at the bottom is determined by "how many times it bounced to the left." If left and right are exactly equally likely, the probability of reaching the middle bin (roughly half the bounces to the left) is the highest, while the probability of reaching either end (all left or all right) is very low. This is the binomial distribution, and as the number of peg rows increases, it gets closer to a smooth bell shape (normal distribution).
Number of peg rows10
Beads dropped: 0
💡 In fact, values created by many small, independent random factors, such as height, test scores, and measurement errors, almost all follow this kind of bell shape. Mathematicians call this the Central Limit Theorem.