Name:
Assigned TF and Section time:
Statistics 100 Quiz 3
Wednesday 23 March 2011
At the DanaFarber 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 DanaFarber staff is the same as the
national prevalence (i.e., 0.0005), what is the probability that a randomly chosen
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 Spring '11
 Grandal
 Statistics, DanaFarber Cancer Institute

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