Marty\'s Barber Shop has one barber. Customers have an arrival rate of 2 custome

Question

Marty's Barber Shop has one barber. Customers have an arrival rate of 2 customers per hour, and haircuts are given with a service rate of 8 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? Round your answer to four decimal places.

P0 = _____

What is the probability that one customer is receiving a haircut and no one is waiting? Round your answer to four decimal places.

P1 = _____

What is the probability that one customer is receiving a haircut and one customer is waiting? Round your answer to four decimal places.

P2 = _____

What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places.

P3 = ______

What is the probability that more than two customers are waiting? Round your answer to four decimal places.

P(More than 2 waiting) = _____

What is the average time a customer waits for service? Round your answer to four decimal places.

Wq = _________minutes

Explanation / Answer

Arrival rate (A) = 2

Service rate (S) = 8

P0 (Probability of zero person in system) = 1 - A/S = 1 - 2/8 = 6/8 = 0.75

P1 (Probability of one person in system) = P0*(A/S) = 0.75*(2/8) = 0.1875

P2 (Probability of two person in system) = P0*(A/S)^2 = 0.75*(2/8)^2 = 0.0469

P3 (Probability of three person in system) = P0*(A/S)^3 = 0.75*(2/8)^3 = 0.0117

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