A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2024 · Q34 Marks
In a certain lottery, on average 1 in every 10000 tickets is a prize-winning ticket. An agent sells 6000 tickets.
- (a)Use a suitable approximating distribution to find the probability that at least 3 of the tickets sold by the agent are prize-winning tickets.[3]
- (b)Justify the use of your approximating distribution in this context.[1]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [B1] [λ =] 0.6 Mean = 0.6 seen.
- [M1] 1 - e^(-0.6) (1 + 0.6 + 0.6²/2) or 1 - e^(-0.6) (1 + 0.6 + 0.18) or 1 - (0.5488 + 0.3293 + 0.09879) Any λ Allow one end error. Must see expression. Accept correct ∑ notation.
- [A1] = 0.0231 SC 0.0231 and no working seen scores B1 (could be implied). SC use of binomial scores M1A1 for 0.0231.
- [B1] 6000 > 50 and either np = 0.6 < 5 or 1/10000 < 0.1 Must state values of n and either np or p. Note: 'n large, p small' is insufficient.
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