Central Limit Theorem


Main Idea

The Central Limit Theorem states that if the sample size (n) is greater than or equal to 30, even if the population is not normally distributed, the sampling distribution for x̅ is approximately normal. 

 If n ≥ 30,  then x̅ ~ N ( μ, \(σ \over {\sqrt n}\) )

 

The Central Limit Also Tells Us... 

1. If the population is not normal and n < 30, then one canNOT assume that the distribution of x̅ is approximately normal.

2. If the population is normal, for any sample size (n can be < 30), one CAN assume that the distribution of x̅ is approximately normal.

 

*For more information on the sampling distribution of x̅, click here