Explain the central limit theorem.

It is a method to find probabilities with sample meAns. From this theorem the the mean of a sample should be close to the mean of a population. The larger the sample the closer to the mean and the smaller the standard deviation.

**Central limit theorem** says that the mean of a large random sample from a population is like a single observation from a population having a normal distribution. The larger the sample the more the sampling distribution resembles a normal distribution.

For any population distribution with mean μ and standard deviation σ, the sampling distribution of the sample mean X is approximately normal with mean μ and standard deviation σ/√n, and the approximation improves as n increases. This is called the **Central limit theorem**.

When you sum or average n randomly selected values from any distribution, normal or otherwise, the distribution of the sum or average is approximately normal, provided that n is sufficiently large.