Buzz Salon has one hair stylist. Customers have an arrival rate of 1.9 customers per hour, and haircuts are given with a service rate of 4.1 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions. (Round your answers to four decimal places.) (a) What is the probability that no units are in the system? (b) What is the probability that one customer is receiving a haircut and no one is waiting? (c) What is the probability that one customer is receiving a haircut and one customer is waiting? (d) What is the probability that one customer is receiving a haircut and two customers are waiting? (e) What is the probability that more than two customers are waiting? (f) What is the average time (in hours) a customer waits for service?
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ρ = λ / μ = 1.9 / 4.1 = 0.4634 (b) The probability that one customer is receiving a haircut and no one is waiting is given by the formula P(1) = ρ^1 * (1 - ρ) = 0.4634^1 * (1 - 0.4634) = 0.2481 Show more…
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