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.
  1. A jar has two red marbles and a green marble.
  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.
  3. ACT scores are approximately normally distributed with mean 20 and standard deviation of 6.
  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 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%?