The sensitivity of a medical test is the probability of it giving a positive result when the patient actually has the disease. The specificity of a medical test is the probability of it giving a negative result when the patient doesn't have the disease.

The proportion of people who have the disease in a particular community is 3 percent. The sensitivity of a test for this disease is 96 percent and the specificity is 92 percent.

a. Find the proportion of positive tests that will occur when the population is tested.

b. What is the probability that a person who tests positive has the disease?

c. Repeat the question if instead of being used as a screening test in a population with a risk of disease of 3 percent the test is instead used for patients who are thought to be 95-percent certain to be suffering from the disease. POLI967