Central Limit Theorem

If a population has a mean of μ, a variance of σ² and takes samples of size n, the means of these samples are approximately the distribution:

Central Limit Theorem Formula

N(0, 1)Central Limit Theorem Formula

The higher the value of n, the better the approximation.


1.The calculation of the probability that the mean of a particular sample is at a certain interval.

2.The calculation of the probability that the sum of the elements of a sample is a priori in a certain interval.

3.The calculation of the mean of the population from a sample.


Bags of salt that are hand packed at a shop have a μ of 500 g and a σ of 35 g. The bags are packed in boxes of 100 units.

1.Calculate the probability that the mean weight of the bags in a box is less than 495 g.

Central Limit Theorem Operations

CLT Operations

Statiscal Solution