A department store has a tailoring service for its customers. Customers in need of this service arrive according to a Poisson process with a mean arrival rate of 24 per hour. Service is provided on a first-come-first-served basis by one tailor. There are 4 chairs provided for customers, but all arriving customers wait elsewhere for their service because it is free of charge only on the day of purchase. The time for a service exhibits an exponential distribution with a mean of 2 minutes. a) What is the average number of customers in the tailoring department? b) What is the probability that a given customer will wait for the tailoring service for more than 10 minutes? c) What is the probability that there will be at least one empty chair?
Added by Matthew M.
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Given: λ = 24 customers per hour μ = 30 customers per hour (1 customer every 2 minutes) Average number of customers in the tailoring department = λ/(μ - λ) = 24/(30 - 24) = 24/6 = 4 Therefore, the average number of customers in the tailoring department is 4. Show more…
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