The number of customers entering a certain branch of a bank on a Monday lunchtime may be modelled by a Poisson distribution with mean 2.4 per minute.

(a) Find the probability that, during a particular minute, four or more customers enter the branch. The probability that a customer, who enters the branch, intends to open a new account is 0.002 and is independent of the intentions of other customers. During a particular morning 450 customers enter the bank.

(b) Use a suitable approximation to find the probability that three or fewer of these 450 customers intend to open new accounts. (AEB)