Central Limit Theorem

The Central Limit Theorem (CLT) is a fundamental statistical principle that states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This theorem is crucial in statistics because it allows for the simplification of complex problems by enabling the use of normal probability techniques. One of the main characteristics of the CLT is that it applies to sufficiently large sample sizes, typically n ≥ 30, which ensures that the sampling distribution of the mean will be approximately normal. Common use cases include hypothesis testing and confidence interval estimation in various fields such as economics, psychology, and quality control.