Problem 7.(12 points)

Students arrive at the administrative services office at an average of one every 10 minutes and their request usually takes about 8 minutes to be processed. Only one clerk staffs the service counter. Assume that student arrival follows a Poisson process, and service time is an exponential random variable.

1. What percentage of time is the server idle? (3 points)

2. How much time, on average, does a student spend waiting in line? (3 points)
3. How long is the queue?(3 points)

4. Whats the probability that an arriving student finds no one in the queue?(3 points)