4.2. Customers arrive at a checkout station in a small grocery store according to a Poisson process of rate A = 1 customer per minute. The checkout station can be operated with or without a bagger. The checkout times for customers are exponentially distributed, and with a bagger the mean checkout time is 30 seconds, while without a bagger this mean time increases to 50 seconds. Suppose the store's policy is to have the bagger help whenever there are two or more customers in the checkout line. In the long run, what fraction of time is the bagger helping the cashier?