See above.The number of batteries sold per week by a garage may be assumed to have a poisson distribution with mean 5.
a) Find the probability that
i)exactly 6 are sold in a randomly chosen week
ii) exactly 6 are sold in each of 3 randomly chosen weeks
iii) exactly 18 are sold in a randomly chosen 3-week period.
b) Find, approximately, the probability that more than 240 are sold in a randomly chosen 52-week period.
OK firstly i write
for a-i i get this
is this agreed?
for part a-ii i'm not sure whether to simply do Right
or rewrite X~Po(15) ...? No, then you would be ignoring the "in each of 3 weeks" part of the problem and just looking at the total number.
part a-iii presents the same problem.
for part b i try
X~Po(5*52) = X~Po(260)
but i'm not sure :/ The approach is right but your arithmetic is wrong.