A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2025 · Q18 Marks
The number, X, of used computers donated to a charity has a constant average rate of 2.4 computers per week.
- (a)State a necessary condition for X to have a Poisson distribution.[1]
- (b)Now assume that X has a Poisson distribution. Calculate the probability that the number of computers donated during a 4-week period is more than 6 and less than 9.[3]
- (c)Use a suitable approximating distribution to calculate the probability that more than 50 computers are donated during a 20-week period.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [1] (a) Computers are donated independently or singly or randomly
- [1] (b) λ = 9.6
- [1] (b) e-9.69.6^7/7! + e-9.69.6^8/8! = e-9.6 (1490.97 + 1789.16) = 0.10098 + 0.12118
- [1] (b) = 0.222 (3 sf)
- [1] (c) N(48, 48)
- [1] (c) 50.5-48/√48 [= 0.361]
- [1] (c) 1 – Φ(‘0.361’)
- [1] (c) = 0.359 (3 sf)
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