The school of business has 3 fax machines.The toner in each machine needs to be changed after about 5 hours of use.There is one unit secretary who is responsible for the fax machine maintenance.It takes him 15 minutes to replace the toner cartridge.What is the probability the system is empty?
A)1.1500
B)1.1658
C).8578
D).8696
E)None of the above

Question

Quizplus · Accepted Answer

The probability that the system is empty can be calculated using the formula for the probability of an empty system in an M/M/1 queue, which is 1 - (arrival rate/service rate). Given the arrival rate is 1/5 per hour (since each machine needs toner every 5 hours) and the service rate is 4 per hour (since it takes 15 minutes to replace the toner), the probability is 1 - (1/5)/(4) = 0.8578.

The School of Business Has 3 Fax Machines