You are designing a quality control system for the waiting time to see a doctor in the emergency room for the DMC. (Danzig Medical Center). You are taking samples of size 5 on the hour every hour and use the waiting time of these patients to draw a control chart. Based on the most recent 20 such samples of size 5, you find the X-double bar to be 45 minutes and R-bar to be 20 minutes. Find the UCL and LCL. If the true mean waiting time has shifted to 60 minutes, what is the probability that you will notice it in the very next sample because of the occurrence of an out of control condition. (Assume that only out of control condition is a sample X-bar falling above UCL or below LCL. ) How many hours will it take on an average for you to look for assignable causes?