Executives of a large discount drug store are concerned with customers balking from the single check-out lines in their stores because they are waiting too long. The executives have set the objective of increasing sales by improving customer check-out service. For that purpose, they have hired a data analytics consultant.

The consultant has studied the operations of a particular store and has learned the following information. Customers get on the single check-out line in the stores at the mean rate of 28 per hour. Once on the line, customers are then served on a first-come, first-served, basis. On average, one cashier, working alone, can check out a customer in two minutes. Working together as a team, an additional cashier reduces the check-out time of a customer by 15 seconds, on average. The manager has also discovered that, on average, customers will balk if their wait is five minutes or more. (Assume Poisson arrivals and exponential service times.)

With the minimum number of cashiers 3 minimum cashiers.

1. state the probability that the check-out line is empty of customers. 

2. state how long, in minutes and seconds, the meantime that customers are expected to have to wait in the check-out line. 

3. In new lines entered below this part, on average, state how many customers are expected to be waiting on line. state how long, in minutes and seconds, is the meantime for a cashier to check out a customer.