Statistics

Normal Distribution

Understand the bell-shaped model, mean, standard deviation and calculator interpretation.

Core idea

A normal distribution is symmetric and bell-shaped. It is determined by the mean \(\mu\) and standard deviation \(\sigma\).

\[ X\sim N(\mu,\sigma^2) \]
μμ+σμ−σNormal distribution
The mean is the centre. The standard deviation measures spread.

Calculator questions

IB AI questions often ask for \(P(X

Language matters: “less than” means left-tail area; “between” means area between two vertical lines.

Worked example

Let \(X\sim N(50,8^2)\). Interpret \(P(42

This is within one standard deviation of the mean, so the probability is approximately \(68\%\).