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Question

during the semester, the library has 12 laptops available for checkout. people arrive to check out a computer once every 0.5 days, with a standard deviation of 1 day; they keep the computers out for an average of 4.5 days, with a standard deviation of 2.5 days. if no computer is available for checkout, the student will be put on a waiting list and will check out a computer once one becomes avaliable.

a) on average, how many computers are available for checkout? (Please show all work)

b) on average how long will a student wait on the waiting list before checking out a computer? (Please show all work)

c) on average, how many students are on the waiting list? (Please show all work)

Solution

a)

on average

computers avaible for checkout = 12*0.5 = 6

b)

on average

students wait on the waiting list before checking out a computer will be

4.5 * 6 = 27 / 60 = 0.45 minutes

c)

how many students are on the waiting list

4.5*0.5 = 2.25 students