The department chair is out of town at a conference and you, as the assistant department chair, find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class. Student arrivals are governed by the Poisson distribution with a mean of 5 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how many students are waiting outside your office door and in your office?
A)0.5
B)1.0
C)1.5
D)2.0

Question

Quizplus · Accepted Answer

The average number of students waiting outside the office door is given by the Poisson distribution with a mean of 5 minutes, which is 5/3 = 1.67 students. The average number of students in the office is given by the exponential distribution with a mean of 3 minutes, which is 3/3 = 1 student. Therefore, the total average number of students waiting outside the office door and in the office is 1.67 + 1 = 2.67 students.

The Department Chair Is Out of Town at a Conference