A rapid test for the presence in the blood of antibodies to HIV, the virus that causes AIDS, gives a positive result with probability about 0.004 when a person who is free of HIV antibodies is tested. A clinic tests 1000 people who are all free of HIV antibodies.
(a) What is the distribution of the number of positive tests?
(b) What is the mean number of positive tests?
(c) You cannot safely use the Normal approximation for this distribution. Explain why.