Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
It is given that 1 in 5000 people in Atalia has this condition. A random sample of 122500 people from Atalia is selected for a medical trial. Let $X$ represent the number who have the condition.
(a)[3]
Use a suitable approximating distribution to find $\mathrm{P}(X \leq 3)$.
(b)[2]
Find the values of $\mathrm{E}(X)$ and $\operatorname{Var}(X)$, and explain how your answers indicate that the approximating distribution used in (a) is likely to be suitable.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate model $X \sim \text{Po}(2.5)$” …