5. Eagle-eyed epidemiology expert Eleanor eagerly, even exhilaratedly, explains every excruciating exigency. Eleanor knows that the Sensitivity of a diagnostic test is the chance it correctly detects the presence of a disease (a carrier tests positive), and the Specificity of a test is the chance it correctly indicates the absence of a disease (a non-carrier tests negative). Eleanor studies the U.S. population where 0.5% of people carry HIV, and a certain very reliable test for HIV is 99% Sensitive and 90% Specific. Consider a population of 100,000 Americans randomly tested for HIV.

a. How many of these 100,000 Americans have HIV?

b. Among those in a. who have HIV, how many test positive?

c. Among those in a. who do Not have HIV, how many still mistakenly test positive? (Called a false positive test.)

d. Among all these Americans who get positive tests, what proportion actually do have HIV?

e. If this test is so reliable, why do you get your answer in part d.?