Question

Suppose that 9% of a population carries antibodies to a virus. For a research project, you need 5 people with antibodies to the virus. How many people must you test to be 95% certain of getting at least 5 people with the antibodies?

This problem will need some trial, and you are trying to find n so that P(X>5)=0.95.
a) 150 people
b) 200 people
c) 250 people
d) 300 people

Answer 1

To find the number of people needed to be tested to be 95% certain of getting at least 5 people with antibodies to the virus, use the binomial distribution.

Step-by-step explanation:

To find the number of people you must test in order to be 95% certain of getting at least 5 people with antibodies to the virus, you can use the binomial distribution. Let X represent the number of people with antibodies in a sample of size n. The probability of getting at least 5 people with antibodies is equal to 1 minus the probability of getting less than 5 people with antibodies. Using a probability distribution table or a calculator, you can find the minimum value of n for which P(X ≥ 5) = 0.95.

In this case, the answer is approximately 250 people, so the correct option is c) 250 people.