Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

At a particular factory, $1$ in $400$ microchips produced are faulty on average. Let $X$ stand for the number of faulty microchips in a random sample of $1000$.
(a)[1]

State which distribution models $X$, and give the values of any parameters.

(b)[2]

State a suitable approximating distribution for $X$, and give the values of any parameters.

(c(i))[2]

Use this approximating distribution to determine $\mathrm{P}(X = 4)$.

(c(ii))[2]

Use this approximating distribution to determine $\mathrm{P}(2 \leq X \leq 4)$.

(d)[3]

Use a suitable approximating distribution to find the probability that, in a random sample of $700$ microchips, there is at least $1$ faulty one.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Take $X$ to be modelled by $B(1000,\tfrac1{400})$

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