Marty’s Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:
a. What is the probability that no units are in the system?
b. What is the probability that one customer is receiving a haircut and no one is waiting?
c. What is the probability that one customer is receiving a haircut and one customer is waiting?
d. What is the probability that one customer is receiving a haircut and two customers are waiting?
e. What is the probability that more than two customers are waiting?
f. What is the average time a customer waits for service?