What is the central limit theorem?

The central limit theorem is a statistical theory that states that the distribution of sample means from a population with any distribution will approximate a normal distribution, as the sample size increases. This theorem is widely used in statistical inference and hypothesis testing, as it allows researchers to make inferences about a population based on a sample of data. The central limit theorem is considered one of the most important concepts in statistics, and it has many practical applications in fields such as finance, engineering, and social sciences.