Centeral Limit Theorem

In some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.

This means we can use statistical methods on normal distributions to analyze data that does not begin as a normal distribution.

Conditions:

  1. Independence: Sampled observations must be independent.
    • Random sample/assignment.
    • If sampling without replacement, then n must be less than 10% of the population.
  2. Sample and Skew: Either the population distribution is normal, or the sample size must be large (usally n>30).