Mathematics 9709 · AS & A Level · The Poisson distribution

The Poisson distribution — practice question

The random variable $X$ gives the number of books taken in by a charity shop each day, and its average rate is fixed at $5.1$ per day.
(a)[1]

State, in context, one condition under which $X$ may be modelled by a Poisson distribution.

(b)[2]

Find the probability that exactly $10$ books arrive in a $3$-day interval.

(c)[4]

Use a suitable approximating distribution to find the probability that more than $180$ books are received during a $30$-day period.

(d)[3]

Find the probability that, in $1$ day, the combined number of books and DVDs received at the shop is greater than $3$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: State that the books are received independently / one at a time / at random

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