Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The random variable $X$ follows the distribution $B(400,\,0.01)$.
(a)[3]
Find $\mathrm{Var}(4X + 2)$.
(b(i))[2]
State a suitable approximating distribution for $X$, including the values of any parameters. Justify why that approximating distribution is appropriate.
(b(ii))[2]
Use the approximating distribution to determine $P(2 \leq X \leq 5)$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying the binomial variance formula gives $\operatorname{Var}(X)=400\times0.01\times0.99$” …