Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
The sales of cell phones at this shop happen one at a time, at random and independently. The mean number sold per hour is $1.2$. Assume now that a Poisson distribution gives an appropriate model.
(a)[1]
State one additional condition that has to hold for the number of sales in a given time interval to be modelled well by a Poisson distribution.
(b)[3]
Find the probability that the number of sales in a randomly selected $12$-hour interval is greater than $12$ but less than $16$.
(c)[4]
Use an appropriate approximating distribution to find the probability that the number of sales in a randomly chosen $1$-month period $(140\text{ hours})$ is below $150$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that the process has a fixed average rate (or constant rate).” …