Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The numbers of cars and trucks per minute arriving at a fuel station are represented by independent variables with distributions $\text{Po}(0.8)$ and $\text{Po}(0.5)$, respectively.
(a)[4]
Use the probability that at least $4$ cars and at least $2$ trucks arrive at the fuel station in a randomly selected $5$-minute interval.
(b)[5]
Apply a suitable approximating distribution to determine the probability that a total of fewer than $145$ cars and trucks arrive at the fuel station in a randomly chosen $2$-hour period.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate evaluation of $1-e^{-4}(1+4+\frac{4^2}{2!}+\frac{4^3}{3!})$” …