Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
Over a $10$-minute interval, the numbers of customers reaching service desks $A$ and $B$ are independently distributed as $\text{Po}(1.8)$ and $\text{Po}(2.1)$ respectively.
(a)[2]
Find the probability that, in a randomly selected $15$-minute period, more than $2$ customers arrive at desk $A$.
(b)[3]
Find the probability that, in a randomly chosen $5$-minute interval, the total number of customers arriving at both desks is less than $4$.
(c)[4]
An inspector is waiting at desk $B$. She wants to wait long enough to be $90\%$ confident of seeing at least one customer arrive at the desk. Find the least time she should wait, giving 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 accurate Poisson expression is $1-e^{-2.7}\left(1+2.7+\dfrac{2.7^2}{2}\right)$” …