Normal Distribution

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The normal distribution is a standard probability density function (PDF) that is often used to model random distributions. It is also known as the Gaussian distribution.

In this article, we will recap what a PDF is, and why it is useful to model distributions with a standard distribution. We will then look at the characteristics of normal distribution and investigate some ways we can use it in real life, including the use of the central limit theorem.

Probability density functions

The normal distribution is usually used to represent continuous, real-valued random variables. For example:

• If we measured the heights of individual people in a population, we could represent these as a PDF. If we then selected an individual at random, the density would tell us the probability that the height of the random individual was within a certain range.
• If we recorded the times of a particular athlete throughout many 100m races, they could also be represented as a PDF. This could be used to estimate the probability that the time of their next race would be between, say, 10.2 and 10.5 seconds.

Taking the second example, here is what the probability density might look like for an athlete running 100m: