The Central Limit Theorem (CLT) is a statistical theory that states that if a large number of independent samples are taken from a population with a mean and standard deviation, the distribution of sample means will approach a normal distribution regardless of the population’s underlying distribution. This means that even if the population is not normally distributed, the distribution of sample means will become approximately normal as the sample size increases.

The CLT is important in statistical inference because it allows us to make assumptions about the population based on the distribution of sample means. Specifically, it allows us to estimate the population mean and standard deviation based on a sample, and to calculate confidence intervals and hypothesis tests. The CLT is widely used in fields such as finance, engineering, and social sciences to make predictions and draw conclusions about large populations based on a sample.

What is the Central Limit Theorem?

Why is the Central Limit Theorem important?

What is the central limit theorem formula?

How is the Central Limit Theorem used in real-world applications?