APPENDIX A Alternative Presentation of the Standard Normal Distribution A3 At first glance, the table on page A1 appears to give areas for positive z-scores only. However, because of the symmetry of the standard normal curve, the table also gives areas for negative z-scores (see Example 1). Using the Standard Normal Table (0-to-z) 1. Find the area under the standard normal curve between z = 0 and z = 1.15. 2. Find the z-scores that correspond to an area of 0.0948. SOLUTION 1. Find the area that corresponds to z = 1.15 by finding 1.1 in the left column and then moving across the row to the column under 0.05. The number in that row and column is 0.3749. So, the area between z = 0 and z = 1.15 is 0.3749, as shown in the figure at the left. 0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 z .00 .01 .02 .03 .04 .05 .06 0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 2. Find the z-scores that correspond to an area of 0.0948 by locating 0.0948 in the table. The values at the beginning of the corresponding row and at the top of the corresponding column give the z-score. For an area of 0.0948, the row value is 0.2 and the column value is 0.04. So, the z-scores are z = -0.24 and z = 0.24, as shown in the figures at the left. z .00 .01 .02 .03 .04 .05 .06 0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 TRY IT YOURSELF 1 1. Find the area under the standard normal curve between z = 0 and z = 2.19. 2. Find the z-scores that correspond to an area of 0.4850. Answer: Page A43 When the z-score is not in the table, use the entry closest to it. When the z-score is exactly midway between two z-scores, use the area midway between the corresponding areas. In addition to using the table, you can use technology to find the area under the standard normal curve that corresponds to a z-score, as shown at the left using a TI-84 Plus for Part 1 of Example 1. EXAMPLE 1 1.15 z Area = 0.3749 0 −0.24 z Area = 0.0948 0 0.24 z 0 Area = 0.0948 TI-84 PLUS normalcdf(0,1.15) 0.3749280109
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