The Central Limit Theorem

The central limit theorem:

• Mean is μ
• Standard deviation σ
• Consider large random samples from the population (Repetition is Allowed) and sample size is sufficiently large (n >30) 

Then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed.

The formula for central limit theorem can be stated as follows:

and

Where:

μ       =  Population mean
σ       =  Population standard deviation
μx¯   =  Sample mean
σx¯   =  Sample standard deviation
n      =  Sample size