270 CHAPTER 6 Normal Probability Distributions 24. Significance Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) … 0.025 and a value is significantly low if P(x or less) … 0.025. Find the female pulse rates separating significant values from those that are not significant. Using these criteria, is a female pulse rate of 48 beats per minute significantly low? In Exercises 25–28, use these parameters (based on Data Set 1 “Body Data” in Appendix B): • Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. • Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in. 25. Navy Pilots The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in. a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall? b. If the Navy changes the height requirements so that all women are eligible except the shortest 3% and the tallest 3%, what are the new height requirements for women? 26. Air Force Pilots The U.S. Air Force required that pilots have heights between 64 in. and 77 in. a. Find the percentage of men meeting the height requirement. b. If the Air Force height requirements are changed to exclude only the tallest 2.5% of men and the shortest 2.5% of men, what are the new height requirements? 27. Mickey Mouse Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters? b. If the height requirements are changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements? 28. Snow White Disney World requires that women employed as a Snow White character must have a height between 64 in. and 67 in. a. Find the percentage of women meeting the height requirement. b. If the height requirements are changed to exclude the shortest 40% of women and the tallest 5% of women, what are the new height requirements? 29. Designing Helmets Engineers must consider the circumferences of adult heads when designing motorcycle helmets. Adult head circumferences are normally distributed with a mean of 570.0 mm and a standard deviation of 18.3 mm (based on Data Set 3 “ANSUR II 2012”). Due to financial constraints, the helmets will be designed to fit all adults except those with head circumferences that are in the smallest 5% or largest 5%. Find the minimum and maximum head circumferences that the helmets will fit. 30. Designing a Desk A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing a desk, we must consider sitting knee height, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.4 in. and a standard deviation of 1.2 in.; females have sitting knee heights that are normally distributed with a mean of 19.6 in. and a standard deviation of 1.1 in. (based on data from the Department of Transportation). a. What is the minimum desk clearance height required to satisfy the requirement of fitting 95% of men? Why is the 95th percentile for women ignored in this case? b. The author is writing this exercise at a desk with a clearance of 23.5 in. above the floor. What percentage of men fit this desk, and what percentage of women fit this desk? Does the desk appear to be made to fit almost everyone?
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