plumiContinuous distributions: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on S2.3 Continuous distributions, 2019–2025, with its mark scheme and examiner’s report.
Paper
All papers
Exam
All years
All 28 questions on Continuous distributions, as a list
- June 2025, Statistics 2 (S2), Q6 (10 marks): The continuous random variable X is uniformly distributed over the interval [a, b] Given that • P (2 < X < 5) = 3 16 • E (X ) = 6 (a) find the value of a and th
- June 2025, Statistics 2 (S2), Q7 (14 marks): When purchasing a pair of glasses from an optician, customers are offered insurance to cover accidental damage. Past records from the optician show that 30% of
- January 2025, Statistics 2 (S2), Q3 (15 marks): The random variable X has a continuous uniform distribution over the interval [–k, 5k] where k > 0 (a) Find, in terms of k, the probability density function of
- January 2025, Statistics 2 (S2), Q6 (8 marks): The discrete random variable R has the distribution R ~ B (n,p) The mean of R is 200 (a) State the variance of R in terms of p A normal distribution is used as
- October 2024, Statistics 2 (S2), Q1 (8 marks): During an annual beach-clean, the people doing the clean are asked to conduct a litter survey. At a particular beach-clean, litter was found at a rate of 4 item
- October 2024, Statistics 2 (S2), Q4 (9 marks): (i) The continuous random variable X is uniformly distributed over the interval [a, b] Given that • P(X > 27) = 3 4 • Var(X) = 300 (a) find the value of a and t
- January 2024, Statistics 2 (S2), Q1 (16 marks): The manager of a supermarket is investigating the number of complaints per day received from customers. A random sample of 180 days is taken and the results are
- January 2024, Statistics 2 (S2), Q5 (10 marks): The random variable W has a continuous uniform distribution over the interval [–6, a] where a is a constant. Given that Var(W) = 27 (a) show that a = 12 Given t
- October 2023, Statistics 2 (S2), Q3 (9 marks): Every morning Navtej travels from home to work. Navtej leaves home at a random time between 08:00 and 08:15 • It always takes Navtej 3 minutes to walk to the bu
- October 2023, Statistics 2 (S2), Q7 (10 marks): The discrete random variable X is given by X ~ B(n, p) The value of n and the value of p are such that X can be approximated by a normal random variable Y where
- June 2023, Statistics 2 (S2), Q1 (11 marks): In a large population 40% of adults use online banking. A random sample of 50 adults is taken. The random variable X represents the number of adults in the samp
- June 2023, Statistics 2 (S2), Q6 (12 marks): Akia selects at random a value from the continuous random variable W, which is uniformly distributed over the interval [a , b] The probability that Akia selects
- January 2023, Statistics 2 (S2), Q4 (10 marks): The continuous random variable X has probability density function f(x), shown in the diagram, where k is a constant. k x 21k f(x) 20 π 0 (a) Find P(X < 10k) (b)
- January 2023, Statistics 2 (S2), Q5 (14 marks): A company produces steel cable. Defects in the steel cable produced by this company occur at random, at a constant rate of 1 defect per 16 metres. On one day th
- October 2022, Statistics 2 (S2), Q4 (9 marks): The probability that a person completes a particular task in less than 15 minutes is 0.4 Jeffrey selects 20 people at random and asks them to complete the task.
- October 2022, Statistics 2 (S2), Q7 (12 marks): (i) The continuous random variable X is uniformly distributed over the interval [a, b] Given that P(5 < X < 13) = 1 5 and E(X) = 9, find P(3X > a + b) (ii) The
- June 2022, Statistics 2 (S2), Q2 (11 marks): The time, in minutes, spent waiting for a call to a call centre to be answered is modelled by the random variable T with probability density function f otherwis
- June 2022, Statistics 2 (S2), Q3 (10 marks): A point is to be randomly plotted on the x-axis, where the units are measured in cm. The random variable R represents the x coordinate of the point on the x-axi
- January 2022, Statistics 2 (S2), Q1 (11 marks): 1 A local pottery makes cups. The number of faulty cups made by the pottery in a week follows a Poisson distribution with a mean of 6 In a randomly chosen week,
- January 2022, Statistics 2 (S2), Q2 (8 marks): 2 The continuous random variable X has cumulative distribution function given by F( ) x x k x k k k x k x k = − + − 0 4 3 1 3 < > where k is a
- January 2022, Statistics 2 (S2), Q7 (8 marks): 7 The sides of a square are each of length L cm and its area is A cm 2 Given that A is uniformly distributed on the interval [10, 30] (a) find P(L 4.5) (b) fi
- October 2021, Statistics 2 (S2), Q2 (11 marks): (i) The continuous random variable X is uniformly distributed over the interval [a, b] Given that P(8 < X < 14) = 1 5 and E(X ) = 11 (a) write down P(X > 14) (b
- June 2021, Statistics 2 (S2), Q5 (11 marks): A game uses two turntables, one red and one yellow. Each turntable has a point marked on the circumference that is lined up with an arrow at the start of the ga
- June 2021, Statistics 2 (S2), Q6 (10 marks): The random variable Y ~ B(225, p) Using a normal approximation, the probability that Y is at least 188 is 0.1056 to 4 decimal places. (i) Show that p satisfies
- January 2021, Statistics 2 (S2), Q3 (17 marks): The number of water fleas, in 100 ml of pond water, has a Poisson distribution with mean 7 (a) Find the probability that a sample of 100 ml of the pond water do
- January 2021, Statistics 2 (S2), Q5 (14 marks): A piece of wood AB is 3 metres long. The wood is cut at random at a point C and the random variable W represents the length of the piece of wood AC. (a) Find th
- October 2020, Statistics 2 (S2), Q2 (12 marks): In the summer Kylie catches a local steam train to work each day. The published arrival time for the train is 10 am. The random variable W is the train’s actual
- October 2020, Statistics 2 (S2), Q3 (15 marks): A manufacturer produces plates. The proportion of plates that are flawed is 45%, with flawed plates occurring independently. A random sample of 10 of these plat
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel International A Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.