A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour.   It takes an average of 2 minutes to answer a question.   It is assumed that arrivals are Poisson and answer times are exponentially distributed. 3. Find the proportion of the time that the employee is busy. 4. Find the average number of people receiving and waiting to receive information. 5. Find the average number of people waiting in line to get information.

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed.   a. How many customers would you expect to see on the average at the coffee urn? b. How long would you expect it to take to get a cup of coffee?  c. What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria? e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?

Suppose that arrivals to a hairdresser follow a Poisson process with mean 12 customers per hour. Calculate the probabilities of: a) no customers in 20 minutes; b) exactly one customer in 5 minutes; c) exactly 12 customers in a hour; d) fewer than three customers in 10 minutes.