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# What is the Central Limit Theorem?

## What is Central Limit Theorem (CLT)?

The central limit theorem argues that if you select sufficiently enough random samples from a population with a mean and standard deviation, the distribution will follow a normal distribution. Sample sizes equal to or greater than 30 are often considered sufficient for the CLT to hold.

## Example of CLT:

σx = $\frac{\sigma}{\sqrt{n}}$

where,

σ is the population standard deviation,

σx is the sample standard deviation; and

n is the sample size

The waiting time until receiving a text message follows an exponential distribution with an expected waiting time of 2.5 minutes. Find the probability that the mean waiting time for 50 text messages exceeds 1.6 minutes

μ=1.6           σ=1.5        n=50

Using Normal Distribution (n>30)
P(X>2.6) = $P \left ( Z> \frac{2.6-1.6}{\frac{1.5}{\sqrt{50}}} \right )$

## What is Central Limit Theorem (CLT)?

The CLT is significant in statistics because it assumes that the mean sample distribution will be normal in most circumstances. This means that we can use statistical techniques that assume a normal distribution.

Owais Siddiqui
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