plumiStatistical distributions: WJEC A‑Level Maths questions
Every WJEC A-Level Maths exam question on S.4 Statistical distributions, 2018–2025, with its mark scheme and examiner’s report.
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![Summer 2025 Unit 4, question 1: A continuous random variable X is uniformly distributed over the interval [c, d]. The mean and 1. variance of X are 7.5 and 3 respectively. Find the values of c](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u40-jun25-01-qp.webp)
![Summer 2023 Unit 4, question 3: 3 The continuous random variable X is uniformly distributed over the interval [1, d]. a) The 90th percentile of X is 19. Find the value of d. [3] b) Calculate t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u40-jun23-03-qp.webp)
![Summer 2023 AS Unit 2, question 2: 2 A card is selected at random from a pack of 20 cards numbered 1 to 20. What distribution models the number on the card? Give a reason for your answer. [2]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u20-jun23-02-qp.webp)
All 25 questions on Statistical distributions, as a list
- Summer 2025, Unit 4, Q1 (4 marks): A continuous random variable X is uniformly distributed over the interval [c, d]. The mean and 1. variance of X are 7.5 and 3 respectively. Find the values of c
- Summer 2025, Unit 4, Q4 (16 marks): 4. Collectable football cards come in packs. The masses, in grams, of the packs are normally distributed with mean 28.3 and standard deviation 0.3. (a) Calculat
- Summer 2025, AS Unit 2, Q1 (6 marks): 1. Financial transactions on a network occur at an average rate of one every 10 minutes. Transactions occur singly, randomly and independently. (a) Stating an a
- Summer 2025, AS Unit 2, Q2 (4 marks): 2. The probability distribution of a discrete random variable X is given below. x 2 3 4 5 P(X = x) 0·1 0·4 0·3 0·2 Given that X1 and X2 are two independent obse
- Summer 2024, Unit 4, Q2 (8 marks): The smallest angle θ, in degrees, of a right-angled triangle with hypotenuse 8 cm, is uniformly 2. distributed across all possible values. 8 cm (a) Find the mea
- Summer 2024, Unit 4, Q4 (21 marks): 4. Jake works for a parcel delivery company. The masses, in kilograms, of parcels he delivers are normally distributed with mean 2.2 and standard deviation 0.3.
- Summer 2024, AS Unit 2, Q2 (10 marks): A baker sells 3.5 birthday cakes per hour on average. 2. (a) State, in context, two assumptions you would have to make in order to model the number of birthday
- Summer 2023, Unit 4, Q3 (5 marks): 3 The continuous random variable X is uniformly distributed over the interval [1, d]. a) The 90th percentile of X is 19. Find the value of d. [3] b) Calculate t
- Summer 2023, Unit 4, Q4 (15 marks): with mean μ and variance σ2. 0 4 A bakery produces large loaves with masses, in grams, that are normally distributed It is found that 11% of the large loaves we
- Summer 2023, AS Unit 2, Q2 (2 marks): 2 A card is selected at random from a pack of 20 cards numbered 1 to 20. What distribution models the number on the card? Give a reason for your answer. [2]
- Summer 2023, AS Unit 2, Q3 (4 marks): 3 The probability distribution of a discrete random variable X is given below. x 4 8 16 0.3 0.5 0.2 P(X = x) Two independent values of X are generated. Find the
- Summer 2023, AS Unit 2, Q4 (6 marks): 4 Sources of the radioactive element caesium each emit radioactive particles at an average rate of 4 per second. The numbers of emissions are modelled by a Pois
- Summer 2022, Unit 4, Q1 (3 marks): 1 An interview process involves three stages of selection. The first stage involves completing an aptitude test. The scores in the aptitude test are on a contin
- Summer 2022, Unit 4, Q3 (8 marks): 3 Rectangles with perimeter 40 cm are produced randomly. The length, in cm, of the shorter side, X, is uniformly distributed across all possible values of X. a)
- Summer 2022, Unit 4, Q4 (13 marks): 4 In a driving simulator, the stopping distances, in metres, for cars travelling at 20 mph and 30 mph can be modelled by normal distributions with means and sta
- Summer 2022, AS Unit 2, Q2 (4 marks): 2 The probability distribution for X, the lifetime of a light bulb, in hours, is given below. X 256 X x ! 259 259 X x ! 262 262 X x ! 265 265 X x ! 267 267 X x
- Summer 2022, AS Unit 2, Q3 (6 marks): 3 In a study, samples of soil were collected during the summer. Soil samples of dimensions 25 cm × 25 cm × 40 cm were collected for analysis. The study found th
- Summer 2019, Unit 4, Q3 (4 marks): 3 At a fairground, Kirsty throws n balls in order to try to knock coconuts off their stands. Any coconuts she knocks off are replaced before she throws again. K
- Summer 2019, Unit 4, Q4 (12 marks): 4 A company produces kettlebells whose weights are normally distributed with mean 16 kg and standard deviation 0.08 kg. a) Find the probability that the weight
- Summer 2019, AS Unit 2, Q3 (7 marks): 3 The number of patients arriving at the Accident and Emergency (A&E) department of a hospital has a mean of 5.3 per hour. A Poisson distribution is used to mod
- Summer 2018, Unit 4, Q3 (10 marks): 3 Antonio arrives at a train station at a random point in time. The trains to his desired destination are scheduled to depart at 12-minute intervals. a) Assume
- Summer 2018, Unit 4, Q4 (8 marks): 4 Arwyn collects data about household expenditure on food. He records the weekly expenditure on food for 80 randomly selected households from across Wales. Cost
- Summer 2018, AS Unit 2, Q1 (2 marks): The random variable X has the binomial distribution B(16, 0.3). 0 1 Showing your calculation, find P(X = 7). [2]
- Summer 2018, AS Unit 2, Q3 (6 marks): Naomi produces oak tabletops, each of area 4.8 m2. Defects in the oak tabletops occur 0 3 randomly at a rate of 0.25 per m2. a) Find the probability that a rand
- Summer 2018, AS Unit 2, Q4 (9 marks): 4 Edward can correctly identify 20% of types of wild flower. He studies some books to see if he can improve how often he can correctly identify types of wild fl
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