art III. Problem Solving (40 Points, 20 each) Show all your work for each of the problems to obtain partial credits. Correct answers without essential work can only earn at most 2 points. (1) Suppose the length of stay in a chronic disease hospital of a certain type of patient has the mean of 60 days with a standard deviation of 15 days. It is reasonably to assume an approximately normal distribution of the lengths of stay. (Note: For each part of this problem, (ii) label the mean and any specific x value(8) with proper scales and (i) sketch a normal curve (iii) shade the region representing the desired/given probability) (a) If one patient is selected from this group at random, what is the probability that this patient will have a length of stay fewer than 70 days? (b) If one patient is selected from this group at random, what the probability that this patient will have a length of stay betreen 50 and 90 days? (c) If one patient is selected from this group at random, what is the probability that this patient will have a length of stay more than 110 days? (d) Suppose a patient noeds to receive an extra care if he/she stays in the hospital beyond a certain period and the hospital only want to have at most 5% of the patient to receive such an extra care. What is the cut-off length of stay for the chosen patient to receive such an extra care