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    Waiting Line Problem for a Local Bank

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    You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes three minutes to serve a customer. Customers arrive, on average, at a rate of 50 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system. Specifically, you must provide answers to the following questions:
    a. What is the average utilization of the three-teller services system?
    b. What is the probability that no customers are being served by a teller or are waiting in line?
    c. What is the average number of customers waiting in line?
    d. On average, how long does a customer wait in line before being served?
    e. On average, how many customers would be at a teller's station and in line?

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    The solution shows the step-by-step solution to waiting line problems. The solution is compiled in the attached document.