A Level Maths · Statistics · Year 12 and 13
Statistical distributions covers the binomial distribution in Year 12 and the normal distribution in Year 13. Knowing when each model is appropriate matters as much as using the calculator functions.
AS content is usually taught in Year 12. The full A Level adds the Year 13 content.
The cumulative distribution function $F(x)$ for a discrete random variable $X$ is given by $F(1) = 0.2$, $F(2) = 0.7$, and $F(3) = 1$. Find $P(X=2)$.
Then practise: skills to practise · open statistical distributions practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section N | Paper 3, Section B |
| Edexcel 9MA0 | Edexcel topic Statistics 4 | Paper 3, Section A |
| OCR A H240 | OCR reference 2.04 | Paper 2, statistics section |
Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
The discrete random variable $X$ has a probability distribution given by $P(X=1)=0.1$, $P(X=2)=0.3$, $P(X=3)=k$, and $P(X=4)=0.2$. Find the value of $k$.
Mark scheme: in the 48-hour free trial.
The random variable $X$ has probability function $P(X=x) = cx$ for $x = 1, 2, 3, 4$. Find the value of the constant $c$.
Mark scheme: in the 48-hour free trial.
Two independent observations, $X_1$ and $X_2$, are taken from a discrete random variable $X$ with distribution $P(X=1)=0.2$, $P(X=2)=0.5$, and $P(X=3)=0.3$. Find $P(X_1 + X_2 = 4)$.
Mark scheme: in the 48-hour free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
These skills sit in the Statistics unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Statistical distributions can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 3: June 2024, June 2023, June 2022 |
| AQA 7357 | Paper 3: June 2023, June 2022, November 2021 |
| OCR H240 | Paper 2: June 2024, June 2023, June 2022 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Statistical Distributions is part of the A Level Maths content that every board examines: AQA section N, Edexcel Statistics 4, OCR 2.04. It is assessed in AQA Paper 3, Section B; Edexcel Paper 3, Section A; OCR A Paper 2, statistics section.
Both. The AS content, usually taught in Year 12, is: Discrete probability distributions; The binomial distribution B(n, p): conditions, probabilities and cumulative probabilities. The full A Level adds: The normal distribution N(μ, σ²): properties, finding probabilities and unknown μ or σ; Using the normal distribution to approximate the binomial; Choosing a suitable distribution and judging the model.
When there is a fixed number of independent trials, each with two outcomes and the same probability of success. State these conditions in context when a question asks you to justify the model.
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