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# Waiting Line

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Gerry Putz is a graduate assistant at Hoosier State College. As part of his duties, he holds regular office hours each week. The class he helps teach is very large - a requirement for all incoming freshmen - so demand for his services during office hours is fairly heavy and consistent. For a project in his advanced service management class, he had a classmate observe the arrivals of students over a two-week period, and found the time between student arrivals to be exponentially distributed, with a mean of 10 minutes. He also found that it took him 8 minutes on average to help a student, and these times were also exponentially distributed. He feels he is overworked, and wants to apply for a grant to buy a computer, which he expects will decrease the average service time. Before he applies, he wants to know some things....

1) Given the current situation, what is the average time a student will wait in line (Wq) when coming to see Gerry for help during office hours? (Be sure to convert the times given to the rates needed in the equations.)
2) What is the probability that when a student arrives at Gerry's office, she will find no one in line outside the office?

#### Solution Preview

Gerry Putz is a graduate assistant at Hoosier State College. As part of his duties, he holds regular office hours each week. The class he helps teach is very large - a requirement for all incoming freshmen - so demand for his services during office hours is fairly heavy and consistent. For a project in his advanced service management class, he had a classmate observe the arrivals of students over a two-week period, and found the time between student arrivals to be exponentially distributed, with a mean of 10 minutes. He also found that it took him 8 minutes on average to help a student, and these times were also exponentially distributed. He feels he is ...

#### Solution Summary

Calculates average waiting time in line and the probability that there is no one in line.

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