A-LevelMathematicsProbability and statistics9709/63 · May/June 2025 · Q18 Marks

At a certain shop, customers arrive independently and randomly at a constant average rate of 23.4 per hour.

(a)Find the probability that, in a randomly chosen 1-minute period, at least 2 customers arrive.[3]
(b)(i)State a suitable approximating distribution for X, giving the value(s) of any parameter(s).[2]
(b)(ii)Use your approximating distribution to find P(20 < X < 30).[3]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] First B1 only scored if see 0.39.
[M1] Any λ. Allow one end error.
[A1] SC unsupported answer score B1 instead of M1A1.
[B1B1] B1 for N(23.4, ....) B1 for Var(X) = 23.4. Note: marks for (i) cannot be recovered from (ii).
[M1] Attempt to standardise both with their values. Must have square roots. Allow no (or incorrect) continuity correction(s).
[M1] For attempt at area between 20 and 30 consistent with their working.
[A1] SC no working seen can score B2 for 0.622.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, May/June 2025 Paper 6 Variant 3, question 1.

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