3-3 Measures of Relative Standing and Boxplots 135 7. New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes. a. What is the difference between the commute time of 95.0 minutes and the mean commute time? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the commute time of 95.0 minutes to a z score. d. Using the criteria summarized in Figure 3-6 on page 123, is the commute time of 95 minutes significantly low, significantly high, or neither? 8. Word Counts Data Set 14 “Word Counts” includes counts of the numbers of words spoken in a day by couples ranging in age from 18 to 29. The males have a mean of 16,576.1 words with a standard deviation of 7871.5 words. The minimum for the males is 1411 words. a. What is the difference between the 1411 words and the mean number of words? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the count of 1411 words to a z score. d. Using the criteria summarized in Figure 3-6 on page 123, is 1411 words significantly low, significantly high, or neither? Significant Values. In Exercises 9–12, use the range rule of thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high. 9. ACT The ACT test is used to assess readiness for college. In a recent year, the mean ACT score was 21.1 and the standard deviation was 5.2. 10. IQ Scores The Wechsler test is used to measure intelligence of adults aged 16 to 80. The mean test score is 100 and the standard deviation is 15. 11. Designing a Work Station In designing a work desk, it is found that males have sitting knee heights with a mean of 21.4 in. and a standard deviation of 1.2 in. (based on data from the Department of Transportation). 12. Designing Aircraft Seats In the process of designing aircraft seats, it was found that men have hip widths with a mean of 36.6 cm and a standard deviation of 2.5 cm (based on anthropometric survey data from Gordon, Clauser et al.). Comparing Values. In Exercises 13–16, use z scores to compare the given values. 13. Tallest and Shortest Men The tallest adult male was Robert Wadlow, and his height was 272 cm. The shortest adult male was Chandra Bahadur Dangi, and his height was 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is more extreme? 14. Pulse Rates Based on Data Set 1 “Body Data” in Appendix B, males have pulse rates with a mean of 69.6 and a standard deviation of 11.3; females have pulse rates with a mean of 74.0 and a standard deviation of 12.5. All pulse rates are measured in beats per minute. Which pulse rate is more extreme: A male with a pulse rate of 50 or a female with a pulse rate of 99? 15. Birth Weights Based on Data Set 6 “Births” in Appendix B, newborn males have weights with a mean of 3272.8 g and a standard deviation of 660.2 g. Newborn females have weights with a mean of 3037.1 g and a standard deviation of 706.3 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1500 g or a female who weighs 1500 g? 16. Candy Based on Data Set 38 “Candies” in Appendix B, Hershey’s Kisses have a mean weight of 4.5338 g and a standard deviation of 0.1039 g, and Reese’s Cups have a mean weight
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