A rapid test for the presence in the blood of antibodies to HIV, the virus that

Question

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 0.003 when a person who is free of HIV antibodies is tested. A clinic tests 1110 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) Is it possible to safely use the Normal approximation for this distribution? No, the distribution is not binomial. Yes, both np and n(1-p) are small. No, np is too small. Yes, both np and n(1-p) are large. No, n(1-p) is too small.

Explanation / Answer

p = 0.003

n = 1110

a) binomial distribution, with n = 1110 and p = 0.003

b) mean = n * p = 1110 * 0.003 = 3.33

c) no, because np is too small.

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