**Instructions**: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers.
- A jar has two red marbles and a green marble.
- (a) Draw a probability tree diagram that represents the experiment consisting of drawing two marbles in succession without replacement.
- (b) What is the probability that one of the two marbles drawn is green?
- (c) Draw a probability tree diagram that represents the experiment consisting of drawing two marbles in succession with replacement. Combine branches where possible.
- (d) What is the probability now that one of the two marbles drawn is green?
- (e) In which case is it more likely to draw a green marble? Is this what you expected?

- Suppose a screening test for a certain virus is positive 99% of the time for infected people and 3% of the time for uninfected people. Also suppose that 0.5% of the population is infected.
- (a) Draw a probability tree diagram for the experiment that consists of
picking a person, who may be either infected or healthy, at random and then giving the person the test.
- (b) What is the chance that the person is infected?
- (c) What is the chance that the person tests positive even though
the person is not infected?
- (d) What is the chance that the person is not infected even though the test is positive?

- ACT scores are approximately normally distributed with mean 20 and standard deviation of 6.
- (a) What z value does 29 represent?
- (b) Use the table on page 709 to determine the proportion of test-takers
that receive a 29 or better on the ACT test.
- (c) What ACT score must you get if 69.15% of test-takers
received a higher score?

- An American Research Group poll of a nationwide random sample of 2,104 of likely voters was conducted by telephone March 2-5, 2007. It showed
Clinton 42%, McCain 45% (with 10% Undecided). Determine a 95% confidence interval for the 45% McCain figure. Show how you compute your answer.
[You can go to http://americanresearchgroup.com/ to check what confidence interval the pollsters give. Is it the same as what you found?]
- A factory produces widgets. The manager believes that only 2% of the widgets produced are defective. How large a sample should the manager take to be 95% sure that the actual rate of defective widgets is between 1% and 3%?