Problem 1 (10pt) A scientist developed an early diagnostic test for a disease. The test has false positive and false negative rates both equal to 0.5% and 2% respectively. The prevalence of the disease in the population is 1 out of 3000. If the disease is not diagnosed early (using the test), the treatment will cost $25, 000. If it is diagnosed early, there is a preventative treatment which costs only $125 and always succeeds. Assume that everyone whose test came out to be positive will undergo that preventative treatment. Also assume that every diagnosis will be an early diagnosis. Advise the scientist on the maximum price of a diagnostic test, such that it is still cheaper to test everyone than not to test anyone