plumiStatistical distributions: OCR MEI A‑Level Maths questions
Every OCR MEI A-Level Maths exam question on S.4 Statistical distributions, 2018–2025, with its mark scheme and examiner’s report.
Find questions560
![June 2025 AS Paper 2, question 8: The probability function of a discrete random variable X is k r P X ( r ) , 1 2 3 4 , , , , = = = r where k is a constant. (a) Determine the value of k. [2] Two](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun25-08-qp.webp?v=3)
![June 2022 AS Paper 2, question 1: The probability distribution for the discrete random variable X is shown below. x 1 2 3 4 5 X x 0.2 0.15 a 0.27 0.14 P ( ) = Find the value of a. [1]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h63002-jun22-01-qp.webp?v=3)
All 37 questions on Statistical distributions, as a list
- June 2025, Paper 2, Q13 (9 marks): According to the Office for National Statistics, in 2022 the proportion of people in England and Wales aged 16 or over who were married or in a civil partnershi
- June 2025, AS Paper 2, Q8 (4 marks): The probability function of a discrete random variable X is k r P X ( r ) , 1 2 3 4 , , , , = = = r where k is a constant. (a) Determine the value of k. [2] Two
- June 2024, Paper 2, Q6 (5 marks): The probability distribution of the discrete random variable X is shown in the table. x 0 1 2 3 P ( X x ) 0.2 a 3a 0.4 = (a) Calculate the value of the constant
- June 2024, Paper 2, Q12 (7 marks): A survey conducted in 2021 showed that 10% of British adults were vegetarians. A dietitian believes that the proportion of British adults who are vegetarians ma
- June 2024, Paper 2, Q15 (17 marks): Bottles of Fizzipop nominally contain 330 ml of drink. A consumer affairs researcher collects a random sample of 55 bottles of Fizzipop and records the volume o
- June 2024, AS Paper 2, Q12 (6 marks): Data collected in the twentieth century showed that the probability of a randomly selected person having blue eyes was 0.08. A medical researcher believes that
- June 2024, AS Paper 2, Q15 (7 marks): Ali and Sam are playing a game in which Ali tosses a coin 5 times. If there are 4 or 5 heads, Ali wins the game. Otherwise Sam wins the game. They decide to pla
- June 2023, Paper 2, Q4 (5 marks): A biased octagonal dice has faces numbered from 1 to 8. The discrete random variable X is the score obtained when the dice is rolled once. The probability distr
- June 2023, Paper 2, Q16 (8 marks): Research conducted by social scientists has shown that 16% of young adults smoke cigarettes. Two young adults are selected at random. (a) Determine the probabil
- June 2023, Paper 2, Q18 (11 marks): Riley is investigating the daily water consumption, in litres, of his household. He records the amount used for a random sample of 120 days from the previous tw
- June 2023, AS Paper 2, Q9 (6 marks): The table shows the probability distribution for the discrete random variable X. x 1 2 3 4 5 P ( X x ) 0.1 0.3 q 2q 3q = You are given that q is a positive cons
- June 2023, AS Paper 2, Q13 (6 marks): In a report published in October 2021 it is stated that 37% of adults in the United Kingdom never exercise or play sport. A researcher believes that the true pe
- June 2022, Paper 2, Q6 (2 marks): 6 X is a continuous random variable such that X N ( , n v . ) + On the sketch of this Normal distribution in the Printed Answer Booklet, shade the area bounded
- June 2022, Paper 2, Q9 (9 marks): At the beginning of the academic year, all the pupils in year 12 at a college take part in an assessment. Summary statistics for the marks obtained by the 2021
- June 2022, Paper 2, Q11 (10 marks): A die in the form of a dodecahedron has its faces numbered from 1 to 12. The die is biased so that the probability that a score of 12 is achieved is different f
- June 2022, Paper 2, Q13 (8 marks): Records from the 1950s showed that 35% of human babies were born without wisdom teeth. It is believed that as part of the evolutionary process more babies are n
- June 2022, AS Paper 2, Q1 (1 mark): The probability distribution for the discrete random variable X is shown below. x 1 2 3 4 5 X x 0.2 0.15 a 0.27 0.14 P ( ) = Find the value of a. [1]
- June 2022, AS Paper 2, Q8 (11 marks): In 2018 research showed that 81% of young adults in England had never donated blood. Following an advertising campaign in 2021, it is believed that the percenta
- November 2021, Paper 2, Q5 (3 marks): It is known that 40% of people in Britain carry a certain gene. A random sample of 32 people is collected. (a) Calculate the probability that exactly 12 people
- November 2021, Paper 2, Q8 (4 marks): The Normal variable X is transformed to the Normal variable Y. The transformation is y a bx , where a and b are positive constants. = + You are given that X N 4
- November 2021, Paper 2, Q13 (7 marks): At a certain factory Christmas tree decorations are packed in boxes of 10. The quality control manager collects a random sample of 100 boxes of decorations and
- November 2021, Paper 2, Q15 (11 marks): =/ r 1 15 (a) Show that 0 99 . - 0 01 . 1 . [3] = # r 1 Kofi is a very good table tennis player. Layla is determined to beat him. Every week they play one match
- November 2021, AS Paper 2, Q2 (2 marks): Mia rolls a six-sided die 24 times and records the scores. She displays her results in a vertical line chart. This is shown in Fig. 2.1. Scores on a six-sided d
- November 2021, AS Paper 2, Q6 (6 marks): The probability distribution for the discrete random variable X is shown below. x 0 1 2 3 3p2 0.5p2 +2p 1.5p2 + 0.5p 1.5p P(X = x) (a) Determine the value of p.
- November 2021, AS Paper 2, Q12 (8 marks): A manufacturer of steel rods checks the length of each rod in randomly selected batches of 10 rods. 100 batches of 10 rods are checked and x, the number of rods
- November 2020, Paper 2, Q12 (15 marks): In this question you must show detailed reasoning. A 5-sided spinner can give scores of 1, 2, 3, 4 or 5. After observing a large number of spins, Elaine models
- November 2020, AS Paper 2, Q4 (4 marks): In a certain country it is known that 11% of people are left-handed. (a) Calculate the probability that, in a random sample of 98 people from this country, 5 or
- June 2019, Paper 2, Q1 (4 marks): Fig. 1 shows the probability distribution of the discrete random variable X. x 1 2 3 4 5 X x 0.2 0.1 k 2k 4k P ( ) = Fig. 1 (a) Find the value of k. [2] (b) Fin
- June 2019, Paper 2, Q10 (16 marks): Club 65–80 Holidays fly jets between Liverpool and Magaluf. Over a long period of time records show that half of the flights from Liverpool to Magaluf take less
- June 2019, Paper 2, Q15 (6 marks): You must show detailed reasoning in this question. The screenshot in Fig. 15 shows the probability distribution for the continuous random variable X, 2 where X
- June 2019, AS Paper 2, Q5 (8 marks): Each day John either cycles to work or goes on the bus. • If it is raining when John is ready to set off for work, the probability that he cycles to work is 0.4
- June 2019, AS Paper 2, Q8 (10 marks): According to the latest research there are 19.8 million male drivers and 16.2 million female drivers on the roads in the UK. (a) A driver in the UK is selected
- June 2018, Paper 2, Q8 (4 marks): Every morning before breakfast Laura and Mike play a game of chess. The probability that Laura wins is 0.7. The outcome of any particular game is independent of
- June 2018, Paper 2, Q10 (8 marks): The screenshot in Fig. 10 shows the probability distribution for the continuous random variable X, where ^ h. 2 X N , + n v Fig. 10 The area of each of the unsh
- June 2018, Paper 2, Q11 (6 marks): The discrete random variable X takes the values 0, 1, 2, 3, 4 and 5 with probabilities given by the formula P(X = x) = k(x + 1)(6 ‒ x) . (i) Find the value of k
- June 2018, Paper 2, Q13 (10 marks): Each weekday Keira drives to work with her son Kaito. She always sets off at 8.00 a.m. She models her ^ h. journey time, x minutes, by the distribution X N 15 4
- June 2018, AS Paper 2, Q4 (5 marks): The probability distribution of the discrete random variable X is given in Fig. 4. r 0 1 2 3 4 P(X = r) 0.2 0.15 0.3 k 0.25 Fig. 4 (i) Find the value of k. [2]
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every OCR MEI A-Level Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.