Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
Packets contain $15$ screws each. Faulty screws arise at random. A large sample of packets is checked for faulty screws, and the average number of faulty screws in one packet is $1.2$.
(a(i))[2]
Show that the variance of the number of faulty screws in a packet is $1.104$.
(a(ii))[3]
Find the probability that a packet contains at most $2$ faulty screws.
(a(iii))[4]
Determine the probability that exactly $7$ packets contain at least $1$ faulty screw.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $1.2 = 15p$ to obtain $p$.” …