Problem 15-9 (Algorithmic)

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3 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) =
6. What is the average time a customer waits for service? If required, round your answer to four decimal places. W_q = hours