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Homework answers / question archive / Name ______________________ Business Statistics Free Response Questions #4: for Chapter 7 Worth 10 points

Name ______________________ Business Statistics Free Response Questions #4: for Chapter 7 Worth 10 points. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. a) Your company's Human Resources department administers a test of “Executive Aptitude.” They report test grades as zscores, and you got a score of 2.20. What does this mean? b) Your company will admit to the executive training program only people who score in the top 3% on the executive aptitude test. With your z-score of 2.20, did you make the cut? Note: You will need to use technology (preferred) or a table to answer this part. c) What do you need to assume about test scores to find your answer in part b? 2. Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. a) Draw the model for these IQ scores. Clearly label it, showing what the 68–95–99.7 Rule predicts about the scores. b) In what interval would you expect the central 68% of IQ scores to be found? Show work or explain this answer. c) About what percent of people should have IQ scores above 132? Show work or explain this answer. d) About what percent of people should have IQ scores between 84 and 100? Show work or explain this answer. 3. Has the Consumer Price Index (CPI) fluctuated around its mean according to a Normal model? Here are some displays. Is a Normal model appropriate for these data? Explain. 4. Shortly after the introduction of the Belgian euro coin, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 150 heads. Note: A fair coin means 50% heads and 50% tails. Use 0.50 for your p. You will be comparing what you expect against what you observed. a) Use the Normal model to approximate the Binomial to determine the probability of spinning a fair coin 250 times and getting at least 150 heads. You can use Statcrunch on this, but you will want to find the mean and standard deviation first. Show those calculations. b) Do you think this is evidence that spinning a Belgian euro is unfair? Would you be willing to use it at the beginning of a sports event? Explain. 5. In the first quarter of 2017, a group of domestic equity mutual funds had a mean return of 6.8% with a standard deviation of 1.5%. Based on the model N(0.068, 0.015) for quarterly returns, what are the cutoff values for the a) highest 10% of these funds? b) lowest 20%? c) middle 40%? Note: although you will likely use StatCrunch for these, it is a good idea to explain or show what you think you need to enter / find to answer these questions. For wrong answers, it helps me identify if the result you get is due to a small error or a major misconception.