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:
N(0, 1)
The higher the value of n, the better the approximation.
Uses:
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.
Example
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.
