plumiStatistical distributions: AQA A‑Level Maths questions
Every AQA A-Level Maths exam question on N Statistical distributions, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 3, question 14: It is given that X ~ N(9, 1.52) and P(a ≤ X ≤ b) ≈ 95% Identify the correct pair of values of a and b. Tick (✓) one box. [1 mark] a = 4.5 and b = 13.5 a = 6 and](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73573-jun25-14-qp.webp)
![June 2024 Paper 3, question 15: It is given that X ~ B(48, 0.175) 15 (a) Find the mean of X [1 mark] 15 (b) Show that the variance of X is 6.93 [1 mark] 15 (c) Find P (X < 10) [1 mark] 15 (d)](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73573-jun24-15-qp.webp)
![June 2022 Paper 3, question 11: X × N(14, 0.35) Find the standard deviation of X, correct to two decimal places. Circle your answer. [1 mark] 0.12 0.35 0.59 1.78](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73573-jun22-11-qp.webp)
![November 2021 Paper 3, question 11: The random variable X is such that X ≥ B(n, p) The mean value of X is 225 The variance of X is 144 Find p. Circle your answer. [1 mark] 0.36 0.6 0.64 0.8](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/73573-nov21-11-qp.webp)
All 24 questions on Statistical distributions, as a list
- June 2025, Paper 3, Q14 (1 mark): It is given that X ~ N(9, 1.52) and P(a ≤ X ≤ b) ≈ 95% Identify the correct pair of values of a and b. Tick (✓) one box. [1 mark] a = 4.5 and b = 13.5 a = 6 and
- June 2025, Paper 3, Q15 (5 marks): The proportion of diners at a restaurant who are vegan is 20% The number of diners at the restaurant who are vegan can be modelled by a binomial distribution. 1
- June 2025, Paper 3, Q17 (7 marks): A maths teacher holds a revision session every Wednesday. In a random sample of eight Wednesdays, the number of students who attended is listed below. 2 4 3 1 4
- June 2025, Paper 3, Q18 (10 marks): The cholesterol level, X, of an adult can be modelled by a normal distribution with mean 5.7 mmol/l and standard deviation 1.2 mmol/l. 18 (a) The lower quartile
- June 2025, Paper 3, Q20 (9 marks): The oxides of nitrogen emissions, F g/km, of a car registered in 2000 can be modelled by a normal distribution with mean 0.41 and standard deviation 0.07 20 (a)
- June 2024, Paper 3, Q15 (9 marks): It is given that X ~ B(48, 0.175) 15 (a) Find the mean of X [1 mark] 15 (b) Show that the variance of X is 6.93 [1 mark] 15 (c) Find P (X < 10) [1 mark] 15 (d)
- June 2024, Paper 3, Q17 (14 marks): In 2019, the lengths of new-born babies at a clinic can be modelled by a normal distribution with mean 50 cm and standard deviation 4 cm. 17 (a) This normal dis
- June 2023, Paper 3, Q12 (8 marks): It is known that, on average, 40% of the drivers who take their driving test at a local test centre pass their driving test. Each day 32 drivers take their driv
- June 2023, Paper 3, Q15 (11 marks): (a) A random sample of eight cars was selected from the Large Data Set. The masses of these cars, in kilograms, were as follows. 950 989 1247 1415 1506 1680 183
- June 2023, Paper 3, Q16 (9 marks): A farm supplies apples to a supermarket. The diameters of the apples, D centimetres, are normally distributed with mean 6.5 and standard deviation 0.73 16 (a) (
- June 2022, Paper 3, Q11 (1 mark): X × N(14, 0.35) Find the standard deviation of X, correct to two decimal places. Circle your answer. [1 mark] 0.12 0.35 0.59 1.78
- June 2022, Paper 3, Q14 (10 marks): A customer service centre records every call they receive. It is found that 30% of all calls made to this centre are complaints. A sample of 20 calls is selecte
- June 2022, Paper 3, Q18 (11 marks): In a particular year, the height of a male athlete at the Summer Olympics has a mean 1.78 metres and standard deviation 0.23 metres. The heights of 95% of male
- November 2021, Paper 3, Q11 (1 mark): The random variable X is such that X ≥ B(n, p) The mean value of X is 225 The variance of X is 144 Find p. Circle your answer. [1 mark] 0.36 0.6 0.64 0.8
- November 2021, Paper 3, Q16 (4 marks): The discrete random variable X has the probability function P(X = x) = c(7 − 2x) x = 0, 1, 2, 3 k x = 4 0 otherwise 8 > > > > < > > > > : where c and k are cons
- November 2021, Paper 3, Q17 (11 marks): James is playing a mathematical game on his computer. The probability that he wins is 0.6 As part of an online tournament, James plays the game 10 times. Let Y
- November 2021, Paper 3, Q18 (10 marks): A factory produces jars of jam and jars of marmalade. 18 (a) The weight, X grams, of jam in a jar can be modelled as a normal variable with mean 372 and a stand
- November 2020, Paper 3, Q17 (8 marks): The lifetime of Zaple smartphone batteries, X hours, is normally distributed with mean 8 hours and standard deviation 1.5 hours. 17 (a) (i) Find P(X 6= 8) [1 ma
- November 2020, Paper 3, Q18 (14 marks): Tiana is a quality controller in a clothes factory. She checks for four possible types of defects in shirts. Of the shirts with defects, the proportion of each
- June 2019, Paper 3, Q13 (10 marks): Patrick is practising his skateboarding skills. On each day, he has 30 attempts at performing a difficult trick. Every time he attempts the trick, there is a pr
- June 2019, Paper 3, Q17 (12 marks): Elizabeth’s Bakery makes brownies. It is known that the mass, X grams, of a brownie may be modelled by a normal distribution. 10% of the brownies have a mass le
- June 2018, Paper 3, Q11 (1 mark): The table below shows the probability distribution for a discrete random variable X. x 1 2 3 4 5 P(X =x) k 2k 4k 2k k Find the value of k. Circle your answer. [
- June 2018, Paper 3, Q15 (7 marks): Abu visits his local hardware store to buy six light bulbs. He knows that 15% of all bulbs at this store are faulty. 15 (a) State a distribution which can be us
- June 2018, Paper 3, Q16 (12 marks): A survey of 120 adults found that the volume, X litres per person, of carbonated drinks they consumed in a week had the following results: X x = 165:6 X x2 = 26
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