Problem 2. (20pts) Dermatologists at VA hospital have managed to secure two grants totaling $5,000. They would like to spend the money on a survey of their psoriasis patients. The doctors identified three strata: mild, medium, and severe cases of the disease. According to patients' medical records, there are 485 mild cases, 366 medium cases and 134 severe cases. Because of difference in lengths of questionnaires, it has been decided to pay a compensation of $15 to mild cases, $25 to medium cases, and $35 to severe cases. From the past surveys, the estimated standard deviations are 2.2, 4.3, and 6.7, respectively. (a) (10pts) Find an approximate number of patients that should be sampled in each stratum, rounding off to the nearest integer. (b) (10pts) Calculate the total cost of administering the survey with the sample sizes found in part (a). Does it exceed the budget? Propose a solution to avoid going over the budget