Section 7.1 The Standard Normal Curve 291 0.2810. This is the area to the left of z = −0.58. To find the area to the right, we subtract from 1 (see Figure 7.8): Area to the right of z = −0.58 = 1 − Area to the left of z = −0.58 = 1 − 0.2810 = 0.7190 Area = 0.2810 Area = 0.7190 −0.58 Figure 7.8 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ −0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 −0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 −0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 −0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 −0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ Sometimes we need to find the proportion of a population that falls between two values. In these cases, we need to find the area between two z-scores. We can do this using Table A.2 by finding the area to the left of each z-score. The area between the z-scores is found by subtracting the smaller area from the larger area. EXAMPLE 7.4 Finding an area between two z-scores Find the area between z = −1.45 and z = 0.42. −1.45 0.42 Figure 7.9 Solution Step 1: Sketch a normal curve, label the points z = −1.45 and z = 0.42, and shade in the area between them. See Figure 7.9. Step 2: Use Table A.2 to find the areas to the left of z = −1.45 and to the left of z = 0.42. The area to the left of z = −1.45 is 0.0735, and the area to the left of z = 0.42 is 0.6628. Step 3: Subtract the smaller area from the larger area to find the area between the two z-scores: Area between z = −1.45 and z = 0.42 = (Area left of 0.42) − (Area left of −1.45) = 0.6628 − 0.0735 = 0.5893 The area between z = −1.45 and z = 0.42 is 0.5893. See Figure 7.10. 0.42 Area = 0.6628 Area = 0.0735 −1.45 −1.45 Area = 0.5893 −1.45 0.42 Figure 7.10 We start with the area to the left of z = 0.42 and subtract the area to the left of z = −1.45. This leaves the area between z = 0.42 and z = −1.45.
navidi_monk_elementary_statistics_2e_ch7-9
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