Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
In each week, a sports team plays one home match and one away match. For their home fixtures, they score goals at a constant average rate of $2.1$ goals per match. For their away fixtures, they score goals at a constant average rate of $0.8$ goals per match. You may assume that goals are scored at random times and independently of one another.
(a(i))[2]
Find the probability that the team scores a total of $4$ goals across their two matches.
(a(ii))[3]
Find the probability that the team scores a total of $4$ goals, while scoring more in the home match than in the away match.
(b)[4]
Use an appropriate approximating distribution to find the probability that the team scores fewer than $25$ goals in $10$ randomly chosen weeks.
(c)[1]
Justify the use of the approximating distribution in part (b).
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct Poisson expression is $e^{-2.9}\frac{2.9^4}{4!}$” …