Question

Example of central limit theorem with different distributions

Answer 1

The Central Limit Theorem (CLT) is a statistical theory states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

As the sample size increases, the sampling distribution of the mean, X-bar, can be approximated by a normal distribution with mean µ and standard deviation σ/√n where:

µ is the population mean

σ is the population standard deviation

n is the sample size

Three different components of the central limit theorem

(1) Successive sampling from a population

(2) Increasing sample size

(3) Population distribution.