Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
During the morning rush hour on trains, each person is classified as a student with probability $0.36$, an office worker with probability $0.22$, a shop assistant with probability $0.29$, or none of these.
(a(i))[3]
$8$ people on a train during the morning rush hour are selected at random. Find the probability that between $4$ and $6$ inclusive are office workers.
(a(ii))[6]
$300$ people on a train during the morning rush hour are selected at random. Find the probability that between $31$ and $49$ inclusive are neither students nor office workers nor shop assistants.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using the binomial expression $\binom{8}{r}p^r(1-p)^{8-r}$ with $p=0.22$” …