Do you believe that profound deterministic patterns often lie hidden behind seemingly random processes? The Central Limit Theorem in probability theory reveals this secret. This theorem states that when a large number of independent random variables are superimposed, the distribution of their sum will approach a graceful bell-shaped curve—the normal distribution. The Galton pegboard is a classic model for verifying this principle: balls fall from the top, and each time they encounter a row of pegs, they have an equal chance of deflecting to the left or right (this is a binomial distribution). When there are enough balls and the fall is deep enough, the accumulation of each tiny, independent random choice eventually results in a distribution in the bottom collection slot that infinitely approximates a smooth normal distribution curve. This intuitively tells us that in a large number of repeated random events, individual outcomes are unpredictable, but the overall distribution has a stab
