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quiz_03_23mar2011_solution - Name Assigned TF and Section...

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Name: Assigned TF and Section time: Statistics 100 Quiz 3 Wednesday 23 March 2011 At the Dana-Farber Cancer Institute all faculty and staff must take a tuberculosis (TB) test every year. A positive test result suggests that someone has the disease, and a negative test result suggests that they do not have the disease. TB in the US is relatively rare; there are approximately 5 cases per 10,000 people, so the probability of a random individual having TB, i.e. Pr( TB ) , is 0.0005. Tests for TB are quite accurate. The probability of a positive test in someone who does not have the disease is 0.01 and the probability that someone with the disease has a negative test is 0.001. This quiz has two problems; the second problem is on the back page. In solving the problems, you may find it helpful define D + and D - to be, respectively, the events that a staff member has or does not have TB, and T + and T - to be the events, respectively, that a test is positive or negative. 1. (10 points) Assuming that the probability of TB in a Dana-Farber staff is the same as the national prevalence (i.e., 0.0005), what is the probability that a randomly chosen
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