Consider the following four scenarios and provide the answers for the questions under each.

2A.The pharmacist at Holy Cross Hospital, Rebecca, receives 25 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 2 minutes to fill each, following a negative exponential distribution.

a)What is the average number of prescriptions in the queue? Show calculation. (2 points)

2min1 prescription / 60 minutes =30 prescriptions

Rate =25

25 ^2 /30(30-25) =4.1666667

=4.17 The average number of prescriptions in the queue

b) Due to COVID 19 the manager director of the hospital decides to hire a second pharmacist, Steven, who operates at the same speed in filling prescriptions and works independently. The probability of both pharmacists being idle is 41.18%, and the average number of prescriptions in the queue is 0.18.How long will the average prescription spend in the queue? Show calculation