Marty’s Barber Shop has one barber. Customers arrive at the rate of 2.2 customers per hour, and haircuts are given at the average 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 there are no customers in the system?
b) What is the probability that 1 customer is receiving a haircut and no one is waiting?
c) What is the probability that 1 customer is receiving a haircut and 1 customer is waiting?
d) What is the probability that 1 customer is receiving a haircut and 2 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?