Marty's Barber Shop has one barber. Customers have an arrival rate of 1.3 customers per hour, and haircuts are given with a service rate of 3 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? Round your answer to 4 decimal places.

b. What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to 4 decimals.

c. What is the probability that once customer is receiving a haircut and one customer is waiting? Round your answer to 4 decimals.

d. What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to 4 decimals.

e. What is the probability that more than two customers are waiting? Round your answer to 4 decimals.

f. What is the average time a customer waits for service? Round your answer to 4 decimals.