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” …