Question

On average, how many students are in line considering a situation where students arrive randomly at the Book Store to check out Clickers? The arrival rates follow the Poisson distribution with an average arrival rate of 32 students per hour and a constant service rate of 47.3 students per hour.

(A) 15.3 students
(B) 18.7 students
(C) 12.7 students
(D) 21.6 students

Answer 1

To determine the average number of students in line at the Book Store, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system. Hence the correct answer is option A

Step-by-step explanation:

To determine the average number of students in line at the Book Store, we can use Little's Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.

In this case, the average arrival rate is given as 32 students per hour and the service rate is given as 47.3 students per hour.

The average time spent in the system can be calculated by taking the reciprocal of the service rate, which is 1/47.3 hours per student.

Therefore, the average number of students in line would be:

Average number of students in line = Average arrival rate * Average time spent in system

Average number of students in line = 32 students/hour * 1/47.3 hours/student

Average number of students in line ≈ 0.677 students

So, the correct answer is option (A) 0.677 students.