Section A Question 125 marks) der the patient data in table below. Let X denote the hospital number of the selected patient (either 1,2,3, or 4). Hospital 1 2 3 4 Total Total 5892/6991 5640 5047/22852 Leave Without Being Seen (LWBS) 195 270 246 242 953 Admitted 1277 1558 984 666 4485 Not admitted 4420/5163 4728 3821 17414 Suppose that four patients are randomly selected with replacement from the total for hospital 1. (a) Determine the probability of exactly one is LWBS (5 marks) Suppose that patients are randomly selected with replacement from the total for hospital 4. (b) What is the smallest sample size needed so that the probability is at least 90% that at least one patient is LWBS? (10 marks) The arrivals of patients to the hospitals between 1:00 and 2:00 PM follows a Poisson process with the mean of 10.5 (c) What is the probability that no patients arrive between 1:00 and 1:10 pm? (5 marks) (d) Suppose that 20 patients arrive between 1:00 and 1:30 PM. What is the probability that three more patients arrive between 1:30 and 2:00 PM? (5 marks)