Statistics 5 - Central limit theorem

Question 1

What is the central limit theorem?

Answer 1

The mean of any random variable is always approximately normally distributed regardless of the distribution of the original random variable.
The central limit theorem says that if 𝑋₁, 𝑋₂ …, 𝑋ₙ is a random sample of size 𝑛 from a population with mean μ and variance σ², then x̄ is approximately ∼N(μ,(σ²)/𝑛).

Question 2

What can the central limit theorem be used for?

Answer 2

The central limit theory is useful for hypothesis testing for the mean of a normal distribution.