Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

Eggs come packed in boxes of 20, and cracked eggs occur independently; the average number of cracked eggs in a box is $1.4$.
(i)[3]

Calculate the probability that a randomly chosen box contains exactly $2$ cracked eggs.

(ii)[2]

Calculate the probability that a randomly chosen box contains at least $1$ cracked egg.

(iii)[2]

A shop sells $n$ of these boxes of eggs. Find the smallest value of $n$ such that the probability of there being at least $1$ cracked egg in each box sold is less than $0.01$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: State $p=0.07$

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