134 CHAPTER 3 Describing, Exploring, and Comparing Data Statistical Literacy and Critical Thinking 1. z Scores Professional football quarterback Tom Brady is 193 cm tall. Based on statistics for the males from Data Set 1 “Body Data” in Appendix B, his height converts to the z score of 2.66. How many standard deviations is his height above the mean? 2. Waiting Times The boxplots shown below represent customer waiting times (minutes) for two different waiting lines. Which line would you prefer, or does it not make a difference? Explain. 3.Boxplot Comparison Refer to the boxplots shown below that are drawn on the same scale. The top boxplot represents weights (kg) of male U.S. Army personnel in 1988, and the bottom boxplot represents weights (kg) of male U.S. Army personnel in 2012. What story is told by these boxplots? 4. z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why? z Scores. In Exercises 5–8, express all z scores with two decimal places. 5.Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of x = 70.2mm Hg and a standard deviation of s = 11.2mm Hg. a. What is the difference between the highest diastolic blood pressure and the mean of the diastolic blood pressures for females? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the highest diastolic blood pressure to a z score. d. Using the criteria summarized in Figure 3-6 on page 123, is the highest blood pressure significantly low, significantly high, or neither? 6.Diastolic Blood Pressure of Males For the diastolic blood pressure measurements of males listed in Data Set 1 “Body Data” in Appendix B, the lowest measurement is 40 mm Hg. The 153 males have a mean of x = 71.3mm Hg and a standard deviation of s = 12.0mm Hg. a. For males, what is the difference between the lowest diastolic blood pressure and the mean of the diastolic blood pressures? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the lowest diastolic blood pressure to a z score. d. Using the criteria summarized in Figure 3-6 on page 123, is the lowest blood pressure significantly low, significantly high, or neither? 3-3 Basic Skills and Concepts
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