A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2022 · Q36 Marks

1.6% of adults in a certain town ride a bicycle. A random sample of 200 adults from this town is selected.

(a)Use a suitable approximating distribution to find the probability that more than 3 of these adults ride a bicycle.[4]
(b)Justify your approximating distribution.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[B1 B1] 3(a) Use of Poisson. mean = 3.2
[M1] 3(a) 1-e-3.2 (1+3.2+3.2²/2+3.2³/3!) or 1-e-3.2 (1+3.2+5.12+5.46133) or 1 - (0.04076 + 0.1304 + 0.2087 + 0.2226) Allow any λ . Allow one end error.
[A1] 3(a) = 0.397 or 0.398 SC Use of binomial: B1 for answer 0.398 (3 sf). 0.397 or 0.398 with no working scores SC B1.
[B1] 3(b) [Binomial with] [n =] 200 > 50
[B1] 3(b) [np =][200 × 0.016 =] 3.2 < 5 or [p =]0.016 <0.1 If B0 B0 SC n large (or n > 50), and p small or p < 0.1 or np <5 : B1.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2022 Paper 6 Variant 2, question 3.

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