# Central Limit Theorem & Gaussian Distribution — A tidy Examination of their relationship

Gaussian distribution is a probability distribution that is symmetrical and bell-shaped. It is parametrized by its mean and standard deviation, and* it is commonly used to model random variables that arise in natural phenomena *such as the heights of individuals, the weight of objects, and many other physical phenomena.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that describes the behavior of the sample mean of a large number of independent, identically distributed random variables.

**The CLT states that as the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the original distribution.**

This means that if we take a large number of samples from any distribution, and calculate the mean of each sample, the distribution of the sample means will be approximately normal.

The relation between the Normal distribution and the CLT is that the *Normal distribution provides the limiting distribution of the sample mean as the sample size approaches infinity*. This means that if the sample size is large enough, we can assume…