304 CHAPTER 6 Normal Probability Distributions 9. Find the probability that nine males have back-to-knee lengths with a mean greater than 23.0 in. 10. War and Peace The accompanying normal quantile plot was constructed from the FleschKincaid Grade Level scores for pages randomly selected from Leo Tolstoy’s classic novel War and Peace. (Flesch-Kincaid Grade Level scores are measures of the U.S. grade level of education that the reader should have to understand the text.) What does the graph tell us about those scores? 1.Bone Density Test A bone mineral density test is used to identify a bone disease. The result of a bone density test is commonly measured as a z score, and the population of z scores is normally distributed with a mean of 0 and a standard deviation of 1. a. For a randomly selected subject, find the probability of a bone density test score greater than -1.37. b. For a randomly selected subject, find the probability of a bone density test score less than 2.34. c. For a randomly selected subject, find the probability of a bone density test score between -0.67 and 1.29. d. Find Q1, the bone density test score separating the bottom 25% from the top 75%. e. If the mean bone density test score is found for 9 randomly selected subjects, find the probability that the mean is greater than 0.23. 2.Unbiased Estimators a. What is an unbiased estimator? b. For the following statistics, identify those that are unbiased estimators: mean, median, range, variance, proportion. c. Determine whether the following statement is true or false: “The sample standard deviation is a biased estimator, but the bias is relatively small in large samples, so s is often used to estimate s.” 3.Critical Values a. Find the standard z score with a cumulative area to its left of 0.01. b. Find the standard z score with a cumulative area to its right of 0.01. c. Find the value of z0.025. Review Exercises
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