6-2 Real Applications of Normal Distributions 265 x (height) z scale 0.95 m 5 66.2 z 5 0 z 5 1.645 x 5 ? FIGURE 6-14 Finding the 95th Percentile EXCEL INTERPRETATION A door height of 72.5 in. would allow 95% of adults to walk through without bending or hitting heads. The door height of 72.5 in. is well below the height of 80 in. required by the International Residential Code, so more than 95% of adults could walk through doors meeting this requirement without bending or hitting their heads. Step 3: With z = 1.645, m = 66.2 in., and s = 3.8 in., we can solve for x by using Formula 6-2: z = x - m s becomes 1.645 = x - 66.2 3.8 The result of x = 72.451 in. can be found directly with a little algebra, or that result can be found by using the following version of Formula 6-2: x = m + 1z # s2 = 66.2 + 11.645# 3.82 = 72.451 Step 4: The solution of x = 72.5 in. (rounded) in Figure 6-14 is reasonable because it is greater than the mean of 66.2 in. YOUR TURN. Do Exercise 21 “Pulse Rates.”
RkJQdWJsaXNoZXIy NjM5ODQ=