1 . A birdwatcher wishes to model the number of birds arriving at a particular barn per hour. a) State two conditions needed for a Poisson distribution to be a suitable model.

b) The expected number of birds arriving per hour is 7. Assuming the conditions for a Poisson model are met, find the probability that, in a randomly chosen hour during the day, the number of birds arriving at the barn is:

(i) fewer than 4
(ii) at least 7
(iii) exactly 9