Use the information below to answer the following question(s).
A steady stream of eager fresh-faced students waits in line to register for classes before the start of fall semester classes.Students arrive at the rate of 10 per hour and it takes the single clerk on duty an average of 3 minutes to check their student status,and register them for classes.The service time is exponentially distributed.
-What is the average number of students waiting in line?
A)between 0 to 1 student
B)2
C)4
D)6

Question

Quizplus · Accepted Answer

The average number of students waiting in line is given by the formula L = λ^2 / (μ(μ-λ)), where λ is the arrival rate and μ is the service rate. In this case, λ = 10 students per hour and μ = 1/3 students per minute = 20 students per hour. Plugging these values into the formula, we get L = (10^2) / (20(20-10)) = 10 / 200 = 0.05 students. This means that there is an average of 0.05 students waiting in line, which is between 0 and 1 student.

Use the Information Below to Answer the Following Question(s)