Billy's Bank is the only bank in a small town in Arkansas. On a typical Friday an average of 10 customers per hour arrive at the bank to transact business.
There is one single teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times can be described by the exponential distribution. Although this is the only bank in town, some people in the town have begun using the bank in a neighboring town about 20 miles away. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller at Billy's is used, find
(a) The average time in the line.
(b) The average number in the line.
(c) The average time in the system.
(d) The average number in the system.
(e) The probability that the bank is empty.