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 $X \sim \text{Po}(2.5)$

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