Central Limit Theorem Proofs

The Central Limit Theorem (CLT) states that when you take many random samples from any population, the averages of those samples will form a normal distribution, or bell curve, regardless of the population's shape, as long as the sample size is large enough (usually n ≥ 30). Its proof involves concepts from probability and statistics, including the idea that errors or variations in samples tend to balance out. This foundation allows us to make predictions and conduct hypothesis testing in various fields, ensuring that even non-normal populations can be analyzed through their sample means.