1. 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?
2. 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?
3. 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?
4. 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?]
5. 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%?