Problem 15-9 (Algorithmic) 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 4 per hour. Use the Poisson...

Problem 15-9 (Algorithmic)

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 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions:

1. What is the probability that no units are in the system? If required, round your answer to four decimal places.
   
   
   
   P₀
   
   =
   
   
   
   


2. What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.
   
   
   
   P₁
   
   =
   
   
   
   


3. What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.
   
   
   
   P₂
   
   =
   
   
   
   


4. What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.
   
   
   
   P₃
   
   =
   
   
   
   


5. What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.
   
   
   
   P(More than 2 waiting) = f
   
   
   
   


6. What is the average time a customer waits for service? If required, round your answer to four decimal places.
   
   
   
   W_q
   
   =