A small bank has two cashiers dealing with customers wanting to withdraw or deposit cash. For each cashier, the time taken to deal with a customer is a random variable having a normal distribution with mean 150 s and standard deviation 45 s.

(a) Find the probability that the time taken for a randomly chosen customer to be dealt with by a cashier is more than 180 s.

(b) One of the cashiers deals with two customers, one straight after the other. Assuming that the times for the customers are independent of each other, find the probability that the total time taken by the cashier is less than 200 s.

(c) At a certain time, one cashier has a queue of 4 customers and the other cashier has a queue of 3 customers, and the cashiers begin to deal with the customers at the front of their queues. Assuming that the cashiers work independently, find the probability that the 4 customers in the first queue will all be dealt with before the 3 customers in the second queue are all dealt with. (C)