(a)[2]
State two assumptions that must be satisfied for the Poisson model to be valid here.
(b(i))[3]
Find the probability that the number of orders arriving in a randomly selected 3-hour period lies between 3 and 5 inclusive.
(b(ii))[4]
Find the probability that, in two randomly selected 1-hour periods, exactly 1 order arrives in one of the 1-hour periods, and at least 2 orders arrive in the other 1-hour period.
(c)[4]
Use a suitable approximating distribution to find the probability that, in a randomly chosen 36-hour period, there are more orders than the shop can handle, given that the shop can only deal with a maximum of 120 orders in that time.