plumiThe Binomial and Poisson distributions: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on S2.1 The Binomial and Poisson distributions, 2019–2025, with its mark scheme and examiner’s report.
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All 31 questions on The Binomial and Poisson distributions, as a list
- June 2025, Statistics 2 (S2), Q3 (10 marks): A sweet shop produces different coloured sweets and mixes them to sell in small, medium or large bags. The proportion of sweets that are blue is p Each small ba
- January 2025, Statistics 2 (S2), Q1 (11 marks): A researcher repeats, independently, 100 trials of a task. The number of successes is X and the probability of success on each trial is 0.05 (a) Find P(X = 2) (
- January 2025, Statistics 2 (S2), Q4 (10 marks): (i) The probability density function of a continuous random variable X is given by f otherwise ( ) x x x 3 20 1 3 0 (a) Using algebraic integration find E
- January 2025, Statistics 2 (S2), Q5 (10 marks): A meteor shower occurs for several weeks every summer. One Monday night during this meteor shower, Chris goes out to look for meteors and sees an average of 15
- 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), Q2 (12 marks): A multiple-choice test consists of 25 questions, each having 5 responses, only one of which is correct. Each correct answer gains 4 marks but each incorrect ans
- June 2024, Statistics 2 (S2), Q1 (13 marks): 1 A garage sells tyres. The number of customers arriving at the garage to buy tyres in a 10‑minute period is modelled by a Poisson distribution with mean 2 (a)
- June 2024, Statistics 2 (S2), Q5 (12 marks): 5 A receptionist receives incoming telephone calls and should connect them to the appropriate department. The probability of them being connected to the wrong d
- 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), Q2 (8 marks): The length of pregnancy for a randomly selected pregnant sheep is D days where D ~ N(112.4, σ 2) Given that 5% of pregnant sheep have a length of pregnancy of l
- October 2023, Statistics 2 (S2), Q1 (10 marks): Sam is a telephone sales representative. For each call to a customer • Sam either makes a sale or does not make a sale • sales are made independently Past recor
- 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), Q4 (13 marks): (a) Given n is large, state a condition for which the binomial distribution B(n, p) can be reasonably approximated by a Poisson distribution. A manufacturer pro
- June 2023, Statistics 2 (S2), Q7 (12 marks): A bakery sells muffins individually at an average rate of 8 muffins per hour. (a) Find the probability that, in a randomly selected one-hour period, the bakery
- January 2023, Statistics 2 (S2), Q1 (11 marks): A shop sells shoes at a mean rate of 4 pairs of shoes per hour on a weekday. (a) Suggest a suitable distribution for modelling the number of sales of pairs of s
- January 2023, Statistics 2 (S2), Q3 (11 marks): Superbounce is a manufacturer of tennis balls. It knows from past records that 10% of its tennis balls fail a bounce test. (a) Find the probability that from a
- 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), Q1 (11 marks): Bhavna produces rolls of cloth. She knows that faults occur randomly in her cloth at a mean rate of 1.5 every 15 metres. (a) Find the probability that in 15 met
- June 2022, Statistics 2 (S2), Q1 (10 marks): The independent random variables W and X have the following distributions. W ~ Po X ~ B(3, 0.8) (a) Write down the value of the variance of W (b) Determine the
- June 2022, Statistics 2 (S2), Q5 (10 marks): The number of particles per millilitre in a solution is modelled by a Poisson distribution with mean 0.15 A randomly selected 50 millilitre sample of the soluti
- June 2022, Statistics 2 (S2), Q7 (12 marks): A bag contains 10 counters each with exactly one number written on it. There are 6 counters with the number 7 on them There are 3 counters with the number 8 on
- 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), Q5 (14 marks): 5 Applicants for a pilot training programme with a passenger airline are screened for colour blindness. Past records show that the proportion of applicants iden
- October 2021, Statistics 2 (S2), Q1 (14 marks): A research project into food purchases found that 35% of people who buy eggs do not buy free range eggs. A random sample of 30 people who bought eggs is taken.
- October 2021, Statistics 2 (S2), Q4 (15 marks): The number of cars entering a safari park per 10-minute period can be modelled by a Poisson distribution with mean 6 (a) Find the probability that in a given 10
- June 2021, Statistics 2 (S2), Q1 (14 marks): Spany sells seeds and claims that 5% of its pansy seeds do not germinate. A packet of pansy seeds contains 20 seeds. Each seed germinates independently of the o
- June 2021, Statistics 2 (S2), Q2 (15 marks): Luis makes and sells rugs. He knows that faults occur randomly in his rugs at a rate of 3 every 4 m2 (a) Find the probability of there being exactly 5 faults in
- January 2021, Statistics 2 (S2), Q1 (14 marks): Jim farms oysters in a particular lake. He knows from past experience that 5% of young oysters do not survive to be harvested. In a random sample of 30 young oy
- 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
- 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
- October 2020, Statistics 2 (S2), Q4 (16 marks): In a peat bog, Common Spotted-orchids occur at a mean rate of 4.5 per m2 (a) Give an assumption, not already stated, that is required for the number of Common S
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