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.
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AS content is usually taught in Year 12. The full A Level adds the Year 13 content. Sitting AS exams or mocks? See the AS Level Maths checklist.
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.
Try it: normal distribution calculator · inverse normal calculator · binomial distribution calculator (free, shows the working)
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 |
| Edexcel 9MA0 | Edexcel topic Statistics 4 | Paper 3, Section A |
| OCR A H240 | OCR reference 2.04 | Paper 2, statistics section |
Statistics questions can be set in the context of your board's large data set: large data set guides and practice (Edexcel · AQA · OCR A).
Three examples from the question bank, one with its full mark scheme open. 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 7-day 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 $c$.
Every question here has a full worked solution. See them all →
The lengths of a species of fish are normally distributed with mean $\mu$ cm and standard deviation $\sigma$ cm. $10\%$ of the fish are longer than $80$ cm and $20\%$ are shorter than $60$ cm. Find the values of $\mu$ and $\sigma$.
Mark scheme: in the 7-day 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.
Full question sets with mark schemes: normal distribution questions (30) · normal approximation to the binomial questions (12)
Revision notes: Discrete distributions and the binomial distribution · The normal distribution
The points lie on the curve of a normal distribution. Change m (the mean) and s (the standard deviation) until the curve passes through every point. What does changing m do to the curve? What does changing s do?
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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 2025, June 2024, June 2023 |
| AQA 7357 | Paper 3: June 2025, June 2024, June 2023 |
| OCR H240 | Paper 2: June 2025, June 2024, June 2023 |
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; 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.
Stretch yourself: original probability problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S34 · Problem S107 · Problem S101 · Problem S29. All 20 →
Formulas in this topic: Binomial distribution · Normal distribution. All formulas A–Z
Applying for maths at university? Taking STEP? STEP-style problems: Probability and statistics. STEP preparation →
Thinking about an EPQ? Maths EPQ ideas that use this topic: Modelling a school canteen queue · Why do opinion polls miss? · P-values and the replication crisis · all 93 ideas
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