Uses of Central Limit Theorem

When we are given a sample mean and we have to approximate with error what could be the population mean (μ) . Whenever we approximate the population mean there is going to be an error associated with it because we are not considering the entire population but only a sample out of it . The population mean with the error forms a Confidence interval or population mean range.How much will this error be depends on the Z* which depends on your confidence level.

The Confidence Interval is given by the formula

Z* can be found out by looking for value of Cumulative Probability associated with Confidence Level in Z-Table. The most commonly used Confidence levels and associated Z* scores are:

If you select say some other confidence Level, your Z will change and so will change your error and hence your population mean range (confidence interval).

So, depending on the confidence level you chose, you will give a different range (confidence interval) for population mean.

The kind of situation where this proves helpful is when you need to find out that at a given confidence level a particular population whether a particular mean value lies within the population mean range associated with the confidence level