Problem: Diagnostic tests of medical conditions can have several results.

1. The patient has the condition and the test is positive (+)
2. The patient has the condition and the test is negative (-) – Known as "false negative"
3. The patient doesn’t have the condition and the test is negative (-)
4. The patient doesn’t have the condition and the test is positive (+) – Known as "false positive"

Consider the following:

Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV,

the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is

not always correct. Suppose that 1% of a large population carries antibodies to HIV in their blood. Of

those that carry the HIV antibodies in their blood, 99.85% will have a positive test result and 0.15% will

have a false-negative test result. Of those that do not carry the HIV antibodies in their blood, 99.4% will

have a negative test result and 0.60% will have a false-positive test result.

1. Draw a tree diagram for selecting a person from this population and testing his or her blood. Take a
   look at figure 15.5 on page 398 of the text.
2. Construct a contingency table that shows the distribution of individuals in this population with
   respect to the presence of antibodies and test results.
3. What is the probability the EIA is positive for a randomly chosen person from this population?
4. Given that the EIA test is positive, what is the probability that a person has the antibody?

e) Given that the EIA test is negative, what is the probability that a person has the antibody?

Problem: Suppose that, as reported by the Center of Disease Control, about 30% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies.

1. Out of the 120 students selected, how many would you expect to be smokers?
2. What would you expect the standard deviation of the number of smokers to be out of the 120 randomly selected?
3. The number of smokers among 120 randomly selected students will vary from group to group (i.e. different groups of 120 students may have a different number of smokers in each group). Explain why the distribution of the number of smokers in a sample size of 120 can be described with a Normal model.
4. Using the 65-95-97.7 Rule, create and interpret a model for the number of smokers among your group of 120 students.

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