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 $p=0.07$” …