Cell-phone sales occur singly, randomly and independently.

(a) State one further condition for the number of sales in a time period to be well modelled by a Poisson distribution. [1]

The average rate is 1.2 sales per hour. Assume a Poisson model is suitable.

(b) Find the probability of more than 12 and fewer than 16 sales in a randomly chosen 12-hour period. [3]

(c) Use a suitable approximation to find the probability of fewer than 150 sales in a randomly chosen month of 140 hours. [4]