One of the most important distributions of probability theory is the Normal Distribution, which is also known as the Gaussian Distribution and the Bell Curve.

It is often used to represent random variables, whose distributions are not known and is an essential component of the Central Limit Theorem.This distribution looks at the mean of the observations and how far apart each observation are with respect to each other.

A great example where the Normal Distribution plays a role is in Rolling a Dice. If a dice is rolled many times, the normal distribution shows that the odds of getting any one the numbers 1:6, is actually 1/6. However the sample size has to be large enough to inference that hypothesis.

The distribution relies on parameters, the mean and the standard deviation. And is usually represented as N(mean, variance)

The Normal Distribution’s simplest form is the Standard Normal Distribution, where the mean is equal to 0 and the variance is equal to 1. The notation for the Standard Normal Distribution follows as N(0,1). Examples of various Normal Distributions, with varying mean and standard deviation, are plotted to see how they change.

By changing the mean, we see that the Normal Distribution shfted along the x-axis by 5 units to the right. Replacing the mean by any value, shifts the distribution along the x-axis. It is important to understand what a mean is before we implement Normal Distributions.

Mean

Definition: In statistics, an average is defined as the number that measures the central tendency of a given set of numbers. There are a number of different averages including but not limited to: mean, median, mode and range.

In addition, increasing the variance shows that the distribution covers a larger range along the x-axis. It is important to understand why the distribution does this as the variance increases.

Variance

Definition: In probability theory and statistics, variance measures how far a set of numbers are spread out. A variance of zero indicates that all the values are identical.