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 \(\sigma\).
\[ X\sim N(\mu,\sigma^2) \]
Calculator questions
IB AI questions often ask for \(P(X\lt k)\), \(P(a\lt X\lt b)\), or an unknown value \(k\) given a probability.
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 \(P(42\lt X\lt 58)\).
This is within one standard deviation of the mean, so the probability is approximately \(68\%\).