The Lindeberg-Levy Central Limit Theorem

The Lindeberg-Levy Central Limit Theorem states that if you take many independent random samples from any distribution with a finite mean and variance, then as the sample size grows large, the distribution of their average will approach a normal (bell-shaped) distribution. This means that even if the original data isn’t normally distributed, the average of a large number of such data points will tend to be normally distributed, making it easier to analyze and predict outcomes in various fields like statistics, finance, and science.