plumiStatistical distributions: OCR A‑Level Maths questions
Every OCR A-Level Maths exam question on S.4 Statistical distributions, 2018–2025, with its mark scheme and examiner’s report.
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![June 2025 Paper 2, question 10: 1). 10 (a) The random variable W has the distribution B(12, 3 Find P(W H 7). [2] (b) The random variable X has the distribution N(45, 42). Find P(X 2 50). [1] (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-10-qp.webp?v=3)
![June 2024 Paper 2, question 9: (a) The masses, M grams, of bags of flour are modelled by the distribution N(1002, 2.25). Find P(1000 1 M 1 1005). [1] 2 (b) The masses, in grams, of bags of su](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun24-09-qp.webp?v=3)
![June 2024 AS Paper 1, question 4: (a) Write down the term in b5 in the expansion of ( b 12 4 a ) . [1] + (b) A variable X has a binomial distribution such that P(X = 5) is given by the term in p](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h23001-jun24-04-qp.webp?v=3)
![June 2023 Paper 2, question 11: 11 The random variable Y has the distribution N( , n v . ) (a) Find P( Y 2 n ) . [1] - v (b) Given that P( Y 2 45 ) 0 2 . and P( Y 1 2 5 ) 0 . 3 , determine the](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun23-11-qp.webp?v=3)
All 28 questions on Statistical distributions, as a list
- June 2025, Paper 2, Q10 (5 marks): 1). 10 (a) The random variable W has the distribution B(12, 3 Find P(W H 7). [2] (b) The random variable X has the distribution N(45, 42). Find P(X 2 50). [1] (
- June 2025, Paper 2, Q14 (9 marks): The masses of stones on a certain beach are normally distributed with mean 0.36 kg and standard deviation 0.12 kg. (a) Find the probability that two stones chos
- June 2025, Paper 2, Q15 (4 marks): The probability distribution of the random variable X is modelled as follows. • P(X = 1) = p where p is a constant. • P(X = x) = 2P(X = x - 1) for x = 2, 3, 4.
- June 2024, Paper 2, Q8 (6 marks): Sweets from a certain manufacturer are sold in packets. Thirty per cent of the sweets are orange, and these are randomly distributed amongst the packets. Each p
- June 2024, Paper 2, Q9 (8 marks): (a) The masses, M grams, of bags of flour are modelled by the distribution N(1002, 2.25). Find P(1000 1 M 1 1005). [1] 2 (b) The masses, in grams, of bags of su
- June 2024, Paper 2, Q13 (5 marks): At an election last year, 20% of voters in Aytown voted for the Now Party. A researcher plans to test whether the proportion of voters in Aytown who support the
- June 2024, Paper 2, Q14 (8 marks): For a certain value of the constant p, the random variable X has the probability distribution given in the table. x 1 2 3 4 1 1 X = x p p2 P ( ) p 6 2 Two indep
- June 2024, AS Paper 1, Q4 (4 marks): (a) Write down the term in b5 in the expansion of ( b 12 4 a ) . [1] + (b) A variable X has a binomial distribution such that P(X = 5) is given by the term in p
- June 2023, Paper 2, Q9 (6 marks): A school contains 500 students in years 7 to 11 and 250 students in years 12 and 13. A random sample of 20 students is selected to represent the school at a par
- June 2023, Paper 2, Q11 (9 marks): 11 The random variable Y has the distribution N( , n v . ) (a) Find P( Y 2 n ) . [1] - v (b) Given that P( Y 2 45 ) 0 2 . and P( Y 1 2 5 ) 0 . 3 , determine the
- June 2022, Paper 2, Q9 (14 marks): The heights, in centimetres, of a random sample of 150 plants of a certain variety were measured. The results are summarised in the histogram. Frequency density
- June 2022, AS Paper 1, Q9 (10 marks): Last year, market research showed that 8% of adults living in a certain town used a particular local coffee shop. Following an advertising campaign, it was expe
- June 2022, AS Paper 1, Q11 (6 marks): Alex models the number of goals that a local team will score in any match as follows. More Number of goals 0 1 2 3 4 than 4 3 1 8 7 2 Probability 0 25 5 25 25 2
- November 2021, Paper 2, Q14 (11 marks): The probability distribution of a random variable X is modelled as follows. k * x 1 2 3 4 , , , , = x P ( X x ) = = 0 , otherwise where k is a constant. 12 (a)
- November 2021, AS Paper 1, Q12 (7 marks): 1). The probabilities ( 12 The variable X has the distribution B(50, 6 P X r ) for r = 0 to 50 are given = b n by the terms of the expansion of ( a ) for specif
- November 2021, AS Paper 1, Q13 (7 marks): (a) The probability distribution of a random variable X is shown in the table, where p is a constant. x 0 1 2 3 1 1 p 3p P X ( x ) = 12 4 Two values of X are ch
- November 2020, Paper 2, Q11 (9 marks): As part of a research project, the masses, m grams, of a random sample of 1000 pebbles from a certain beach were recorded. The results are summarised in the tab
- November 2020, Paper 2, Q15 (10 marks): In this question you must show detailed reasoning. The random variable X has probability distribution defined as follows. x * 15 2 x 2 3 4 5 , , , , = # 64 x !
- November 2020, AS Paper 1, Q11 (4 marks): In this question you must show detailed reasoning. A biased four-sided spinner has edges numbered 1, 2, 3, 4. When the spinner is spun, the probability that it
- June 2019, Paper 2, Q9 (11 marks): (a) The masses, in grams, of plums of a certain kind have the distribution N(55, 18). (i) Find the probability that a plum chosen at random has a mass between 5
- June 2019, Paper 2, Q12 (12 marks): A random variable X has probability distribution defined as follows. * kx x 1 2 3 4 5 , , , , , = P ( X x ) = = 0 otherwise , where k is a constant. (a) Show th
- June 2019, Paper 2, Q13 (5 marks): It is known that 26% of adults in the UK use a certain app. A researcher selects a random sample of 5000 adults in the UK. The random variable X is defined as t
- June 2019, AS Paper 1, Q11 (8 marks): It is known that, under the standard treatment for a certain disease, 9.7% of patients with the disease experience side effects within one year. In a trial of a
- June 2018, Paper 2, Q8 (8 marks): (i) The variable X has the distribution N(20, 9). (a) Find P(X 2 25). [1] (b) Given that P(X 2 a) = 0.2, find a. [1] (c) Find b such that P(20 - b 1 X 1 20 + b)
- June 2018, Paper 2, Q12 (11 marks): The discrete random variable X takes values 1, 2, 3, 4 and 5, and its probability distribution is defined as follows. Z a x 1 , = ] ] 1 X x X x x P ( ) [ P ( 1
- June 2018, Paper 2, Q13 (12 marks): In this question you must show detailed reasoning. The probability that Paul’s train to work is late on any day is 0.15, independently of other days. (i) The nu
- June 2018, AS Paper 1, Q10 (5 marks): The probability distribution of a random variable X is given in the table. x 0 2 4 6 3 5 4 p p P(X = x) 8 16 (i) Find the value of p. [2] (ii) Two values of X a
- June 2018, AS Paper 1, Q11 (5 marks): The probability that Janice sees a kingfisher on any particular day is 0.3. She notes the number, X, of days in a week on which she sees a kingfisher. (i) State
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