plumiDiscrete distributions and the binomial: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on N.1 Discrete distributions and the binomial, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 15 questions on Discrete distributions and the binomial, as a list
- 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 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 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 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
- 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 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
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