A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2023 · Q55 Marks

In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Following a change in the position of the desk, it is expected that the mean number of enquiries per minute will increase. In order to test whether this is the case, the total number of enquiries during a randomly chosen 5-minute period is noted. You should assume that a Poisson model is still appropriate. Given that the total number of enquiries is 5, carry out the test at the 2.5% significance level.

(a)Given that the total number of enquiries is 5, carry out the test at the 2.5% significance level.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[B1] Or "population mean no. enquiries = 0.31 (per minute)" ое. Allow 'λ = 1.55' or μ = ‘1.55'.
[M1] Allow one end error, e.g. extra term: e-1.55 × 1.555 / 5!.
[A1] Allow 0.021. SC B1 no working scores B1 instead of M1A1.
[M1] For valid comparison.
[A1 FT] In context, not definite. e.g., not "Mean no. of enquiries has increased". No contradictions. Note: e-1.55x 1.555 / 5! = 0.0158 < 0.025: scores max B1

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