# 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.

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