Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

Customers turn up at a certain shop at random times. It has been established that the average number of customers arriving in a $5$-minute period is $2.1$.
(a)[2]

Find the probability that exactly $4$ customers arrive in a $10$-minute interval.

(b)[2]

Find the probability that at least $4$ customers arrive in a $20$-minute interval.

(c)[4]

Use a suitable approximating distribution to find the probability that fewer than $40$ customers arrive during a $2$-hour interval.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: The required probability is $e^{-4.2}\dfrac{4.2^4}{4!}$.

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