Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

The customer counts reaching service desks $A$ and $B$ in a $10$-minute interval are independent, with distributions $\text{Po}(1.8)$ and $\text{Po}(2.1)$ respectively.
(a)[2]

Find the probability that, in a randomly selected $15$-minute interval, more than $2$ customers arrive at desk $A$.

(b)[3]

Find the probability that, in a randomly chosen $5$-minute interval, the combined number of customers arriving at both desks is less than $4$.

(c)[4]

An inspector is waiting at desk $B$. She wants to wait for long enough to be $90\%$ certain of seeing at least one customer arrive at the desk. Find the shortest time she should wait, and give your answer correct to the nearest minute.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: The Poisson expression is $1-e^{-2.7}(1+2.7+\frac{2.7^2}{2})$.

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