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LearnCambridge97092026–2027Paper 5 · Probability & Statistics 1The normal distribution

Paper 5 · Module

The normal distribution

3 subtopics≈ 105 min in total

Start the module: Standardising and normal probabilities Open graphing calculator

Standardising and normal probabilities
Heights, masses and exam marks often follow a symmetric bell-shaped curve. Every normal distribution is the standard one, $Z\sim N(0,1)$ , shifted and stretched, so one table of $\Phi(z)$ answers every question.
≈ 35 min
Inverse normal and finding μ and σ
Run the standardising formula backwards. Turn the probability into a $z$ -value with the tables, then solve $\dfrac{x-\mu}{\sigma}=z$ for whichever quantity is missing.
≈ 35 min
Normal approximation to the binomial
For large $n$ , the binomial's bars trace out a bell curve. Replace $B(n,p)$ by $N(np,npq)$ , widen each whole number into an interval of width $1$ (the continuity correction), and standardise.
≈ 35 min