Problem:

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. Nurse Smith has indicated to her shift supervisor that although she has not kept records she 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 idle more than 40% of the time.

Required:

Question 1) Calculate how many minutes a patient waits on average. , round your answer to 2 decimal places, the tolerance is +/- 0.5.

Question 2) What percent of the time is the nurse idle? %, round your answer to integer, the tolerance is +/- 1.

Question 3) Should a second nurse be assigned (a, b (or) c)?

a) yes, the patient waiting time is more important than percent idle

b) no, the percent busy exceeds 40%

c) no, patients wait less than 10 minutes and the nurse is idle more than 40% of the time

Solve the given numerical problem and illustrate step by step calculation.