Dr. Al Wright has a solo physician practice in Bethesda, MD. The practice only accepts 10 appointments a day, each at the hour. The first appointment is at 8:00AM and the last one at 5:00PM. Due to traffic and other unavoidable travel issues, patients are known to have an arrival time deviation that is Uniformly distributed between -5 minutes and +25 minutes. [For instance, for a patient who has a 2:00PM appointment, his/her actual arrival time is uniformly distributed between 1:55 PM and 2:25 PM]. It has been estimated that the total time a patient spends in Dr. Wright’s clinic (paper-work, consultancy and check-out procedures) is Normally distributed with a mean of 50 minutes and a standard deviation of 10 minutes. If a patient arrives and finds another patient being seen, he/she must wait until the previous patient is done with his/her consultancy. On the other hand, if there is no prior patient being treated, an incoming patient will be taken in immediately (including the first one).
Assume that Dr. Wright and his staff do not take a lunch break and that all ten of the patient appointment slots are always taken. Assume also that all days of the week exhibit similar behavior.
(a) Perform a 5,000-iteration simulation run using @RISK and report the average wait time for a patient.
(b) The practice claims that they are 95% confident that a patient does not have to wait for more than 15 minutes. Is that claim correct?
[You may consider modeling time as minutes since midnight, so that the 8:00 slot becomes 480, 9:00 slot becomes 540, etc.]