The Poisson distribution: Edexcel A‑Level Further Maths questions

Edexcel A-Level Further Maths past-paper questions on 1.2 The Poisson distribution, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 16 questions on The Poisson distribution, as a list

June 2025, Further Statistics 1, Q5 (10 marks): A football team scores goals at an average rate of 1.8 goals per match. (a) Give two assumptions that would be necessary to use a Poisson distribution to model
June 2025, AS Further Statistics 1, Q3 (11 marks): Raoul, Steffi and Taro are catching butterflies for research. The number of butterflies caught by Raoul per hour may be assumed to follow a Poisson distribution
June 2024, Further Statistics 1, Q2 (7 marks): The number of errors made by a secretary is modelled by a Poisson distribution with a mean of 2.4 per 100 words. A 100‑word piece of work completed by the secre
June 2023, Further Statistics 1, Q2 (11 marks): Telephone calls arrive at a call centre randomly, at an average rate of 1.7 per minute. After the call centre was closed for a week, in a random sample of 10 mi
June 2023, AS Further Statistics 1, Q3 (16 marks): A machine produces cloth. Faults occur randomly in the cloth at a rate of 0.4 per square metre. The machine is used to produce tablecloths, each of area A squar
June 2023, AS Further Statistics 1, Q4 (12 marks): Table 1 below shows the number of car breakdowns in the Snoreap district in each of 60 months. Number of car breakdowns 0 1 2 3 4 5 12 11 19 14 3 1 Frequency Ta
June 2022, Further Statistics 1, Q3 (14 marks): During the summer, mountain rescue team A receives calls for help randomly with a rate of 0.4 per day. (a) Find the probability that during the summer, mountain
June 2022, AS Further Statistics 1, Q2 (10 marks): Xena catches fish at random, at a constant rate of 0.6 per hour. (a) Find the probability that Xena catches exactly 4 fish in a 5‑hour period. (2) The probabili
November 2021, Further Statistics 1, Q2 (14 marks): On a weekday, a garage receives telephone calls randomly, at a mean rate of 1.25 per 10 minutes. (a) Show that the probability that on a weekday at least 2 call
November 2020, Further Statistics 1, Q1 (13 marks): The number of customers entering Jeff’s supermarket each morning follows a Poisson distribution. Past information shows that customers enter at an average rate
November 2020, Further Statistics 1, Q2 (4 marks): The discrete random variables W, X and Y are distributed as follows W ~ B(10, 0.4) X ~ Po(4) Y ~ Po(3) (a) Explain whether or not Po(4) would be a good approxim
November 2020, AS Further Statistics 1, Q1 (10 marks): A plumbing company receives call-outs during the working day at an average rate of 2.4 per hour. (a) Find the probability that the company receives exactly 7 ca
November 2020, AS Further Statistics 1, Q4 (8 marks): During the morning, the number of cyclists passing a particular point on a cycle path in a 10-minute interval travelling eastbound can be modelled by a Poisson
June 2019, Further Statistics 1, Q2 (8 marks): Indre works on reception in an office and deals with all the telephone calls that arrive. Calls arrive randomly and, in a 4-hour morning shift, there are on ave
June 2019, AS Further Statistics 1, Q3 (13 marks): Andreia’s secretary makes random errors in his work at an average rate of 1.7 errors every 100 words. (a) Find the probability that the secretary makes fewer th
June 2018, AS Further Statistics 1, Q2 (11 marks): The number of heaters, H, bought during one day from Warmup supermarket can be modelled by a Poisson distribution with mean 0.7 (a) Calculate P(H  2) (1) The n

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