262 CHAPTER 6 Normal Probability Distributions Step 2: We can convert the showerhead height of 72 in. to the z score of 1.21 by using Formula 6-2 as follows: z = x - m s = 72 - 68.6 2.8 = 1.21 1rounded to two decimal places2 Step 3: Technology: Technology can be used to find that the area to the right of 72 in. in Figure 6-12 is 0.1123 rounded. (With many technologies, Step 2 can be skipped. See technology instructions at the end of this section.) The result of 0.1123 from technology is more accurate than the result of 0.1131 found by using Table A-2. Table A-2: Use Table A-2 to find that the cumulative area to the left of z = 1.21 is 0.8869. (Remember, Table A-2 is designed so that all areas are cumulative areas from the left.) Because the total area under the curve is 1, it follows that the shaded area in Figure 6-12 is 1 - 0.8869 = 0.1131. YOUR TURN. Do Exercise 13 “Pulse Rates.” INTERPRETATION The proportion of men taller than the showerhead height of 72 in. is 0.1123, or 11.23%. About 11% of men may find the design to be unsuitable. (Note: Some NBA teams have been known to intentionally use lower showerheads in the locker rooms of visiting basketball teams.) Until recently, the U.S. Air Force required that pilots have heights between 64 in. and 77 in. Heights of women are normally distributed with a mean of 63.7 in. and a standard deviation of 2.9 in. (based on Data Set 1 “Body Data” in Appendix B). What percentage of women meet that height requirement? CP EXAMPLE 2 Air Force Height Requirement SOLUTION Figure 6-13 shows the shaded region representing heights of women between 64 in. and 77 in. x (height) z scale 0.4558 64 m 5 63.7 z 5 0 z 5 0.10 z 5 4.59 77 FIGURE 6-13 Heights of Women
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