## Normal Distribution / Gaussian Distribution

A Random Variable (**X**) having mean () and standard deviation () is said to be Normally Distributed if it has the following properties:

#### Properties of Normal Distribution

- The
**mean**,**median**and m**ode**are all at the centre point. - There is no skewness.
- It has a
**kurtosis**of**3**. - It follows
**Bell Curve.** - It is
**symmetrical**on both sides of the mean. - 50% data lies before the mean and the other 50% is on the right side of the mean.
- The data near the mean is more frequent in occurrence than the data far from it.

#### Empirical Rule

- If you go one standard deviation to the left and one standard deviation to the right, it covers
**68%**of the total data. - If you go two standard deviations to the left and two standard deviations to the right, it covers
**95%**of the total data. - If you go three standard deviations to the left and three to the right, it covers
**99.7%**of the total data.

## Standard Normal Distribution

Standard Normal Distribution is a particular type of Normal Distribution where the **mean is 0** and the **standard deviation is 1**.

### How to convert Normal Distribution into Standard Normal Distribution?

Normal Distribution can be converted to Standard Normal Distribution by using a** z-score**. This process is also called **Standardization**.

z-score =

where

- = mean
- = standard deviation
- = current value

## Central Limit Theorem

The Normal Distribution is key to the central limit theorem. According to it, if multiple samples are taken from a population then the distribution of their sample means will follow a normal distribution as the sample size increases.

## Applications of Normal Distribution

- All kind of variables in nature is nearly normally distributed like height, weight, job satisfaction, body temperature, strength etc.
- The central limit theorem is based on the concept of normal distribution.
- The assumption behind statistical tests is that data follows a normal distribution.
- If a variable is not normally distributed, it can be converted into normal distribution by a simple transformation.

You can check other probability distributions here.