Lucy the librarian manages a small archive office. She learned in Library Management School that her office's visitors tend to arrive according to a Poisson arrival distribution, and the time they spend with Lucy follows an exponential distribution (implying M/M/1 queuing system). Lucy's research indicates that, on average, visitors arrive at a rate of six per hour. It takes Lucy about 6 minutes to assist a visitor with their archive search. With this information, find the percentage of time that Lucy is idle?

 

a. 0.7

 

b. 0.6

 

c. 0.5

 

d. 0.4

 

e. 0.3

 

f. None of these