A Professor's Teaching Assistants Sit in Their Communal Office and Answer

Essay

A professor's teaching assistants sit in their communal office and answer questions from students the afternoon before the final exam. The class is a mass lecture of 350 students, and the teaching assistants have final exams of their own, so they concentrate on providing explanations as quickly as possible. On average, the three teaching assistants can answer 30 questions an hour and students arrive at their office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed.
a. What fraction of their time do the teaching assistants spend answering questions?
b. What is the average number of students waiting outside their office?
c. What is the average time a student spends in line outside the teaching assistants' office and having their question answered?