Question 1: Customers arrive at Paul Harrold’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Paul can perform haircuts at a rate of 5 per hour, distributed exponentially.
a) Find the average number of customers waiting for haircuts.
b) Find the average number of customers in the shop.
c) Find the average time a customer waits until it is his or her turn.
d) Find the average time a customer spends in the shop.
e) Find the percentage of time that Paul is busy
Question 2: Zimmerman’s Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes.
It is assumed that service times may be described by the exponential distribution. 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 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.