Annie Campbell is a nurse on the evening shift from 10:00 P.M. to 6:00 A M. at Community Hospital, She is responsible for 15 patients in her area. She averages two calls from each of her patients every evening (Poisson distributed), and she must spend an average of 10 minutes (negative exponential distribution) with each patient who calls, Nunn Smith has Indicated to her shift supervisor that although she has not kept records the believes her patients must wait about 10 minutes on average for her to respond and she has requested that her supervisor assign a second nurse to her area. The supervisor believes 10 minutes is too long to wait, but she does not want her nurses to be id's more than 40%% of the time, [a) M Incomect. Calculate how many minutes a patient waits on average. Round your answer to 2 decimal places, the tolerance is /- 0.5. What percent of the time is the nurse idle? Round your answer to integer, the tolerance is +/- J.1) Average wait time in the system (Wq) = Lq / Lambda Where Lambda (Arrival rate) = 2 calls per 8 hours = 2 / 8 = 0.25 per hour Mue (Service rate) = 10 minutes per call = 6 per hour Lq = Lambda?/Mue(Mue-Lambda) = 0.252 / 6(6-0.25) = 0.0018 So Average wait time of a patient in the system = Lq/Lambda = 0.0018 / 0.25 = 0.0072 ~ 0.01 minutes 2) Percent Idle time = 100% - Utilization Where Utilization = Lambda / Mue x 100 = 0.25/6 * 100 = 0.0416 * 100 = 4.1 ~ 4% So Percent Idle time = 100%-4% = 96%