A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2021 · Q24 Marks

The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all.

(a)Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[B1] N(45.2, 45.2) (SOI)
[M1] (60.5-45.2) / √45.2 [= 2.276] (Allow with wrong or no continuity correction.)
[M1] 1 – Φ('2.276')
[A1] 0.0114

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2021 Paper 6 Variant 1, question 2.

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