294 Chapter 7 The Normal Distribution EXAMPLE 7.9 Finding the z-score corresponding to an area to the right Use Table A.2 to find the z-score that has an area of 0.68 to its right. −0.47 Area = 0.68 Figure 7.12 Solution Step 1: Sketch a normal curve and shade in the given area. Step 2: Determine the area to the left of the z-score. Since the area to the right is 0.68, the area to the left is 1 − 0.68 = 0.32. Step 3: In Table A.2, look through the body of the table to find the area closest to 0.32. This value is 0.3192. The z-score in Table A.2 corresponding to an area of 0.3192 is z = −0.47. See Figure 7.12. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ −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 −0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ EXAMPLE 7.10 Using technology to find the z-score corresponding to an area to the right In Example 7.9, we found the z-score that has an area of 0.68 to its right. Use technology to find this z-score. Solution We use the TI-84 Plus calculator. The first two steps are the same as those for using the table. We must first find the area to the left of the desired z-score, by subtracting the area to the right from 1. Since the area to the right is 0.68, the area to the left is 1 − 0.68 = 0.32. The results are as follows. Step-by-step instructions are given in the Using Technology section on page 296. The TI-84 Plus gives z = −.4676988012. Rounding to two decimal places gives z = −0.47. Check Your Understanding 5. Use Table A.2 to find the z-score with an area of 0.45 to its left. −0.13 6. Use Table A.2 to find the z-score with an area of 0.37 to its right. 0.33 7. Use any method to find the z-score with an area of 0.74 to its left. 0.64 8. Use any method to find the z-score with an area of 0.09 to its right. 1.34 Answers are on page 299.
navidi_monk_elementary_statistics_2e_ch7-9
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