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 0.005 when a person who is free of HIV antibodies is tested. A clinic tests 1170 people who are all free of HIV antibodies.

(a) What is the distribution of the number of positive tests?

---Select--- (approximately normal, binomial standard normal, normal) with n =  and p =  (Use 3 decimal places.) ______

(b) What is the mean number of positive tests?
(Use 2 decimal places.) ______

(c) Is it possible to safely use the Normal approximation for this distribution?

1. Yes, both np and n(1-p) are small.

2. No, n(1-p) is too small.    

3. No, np is too small.

4. No, the distribution is not binomial.

5. Yes, both np and n(1-p) are large.

Explanation / Answer

a) binomial with n=1170 and p=0.005

B) mean = np = 1170×0.005 = 5.85

C) ans is 3) No, np is too small. It should at least 10 to be approximately normal.

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