8.40 AIDS test A test for the presence of antibodies to the AIDS virus in blood has proba-
bility 0.99 of detecting the antibodies when they are present. Suppose that during a year
20 units of blood with AIDS antibodies pass through a blood bank.
(a) Take X to be the number of these 20 units that the test detects. What is the distribution
of X?
(b) What is the probability that the test detects all 20 contaminated units? What is the prob-
ability that at least 1 unit is not detected?
(c) What is the mean number of units among the 20 that will be detected? What is the stan-
dard deviation of the number detected?
