238 CHAPTER 5 Normal Probability Distributions 1.15 z Area = 0.8749 0 −0.24 0 z Area = 0.4052 Using the Standard Normal Table 1. Find the cumulative area that corresponds to a z@score of 1.15. 2. Find the cumulative area that corresponds to a z@score of -0.24. 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 0.8749. So, the area to the left of z = 1.15 is 0.8749, as shown in the figure at the left. 0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 z .00 .01 .02 .03 .04 .05 .06 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 You can use technology to find the cumulative area that corresponds to z = 1.15, as shown at the left. Note that to specify the lower bound, use -10,000. 2. Find the area that corresponds to z = -0.24 by finding -0.2 in the left column and then moving across the row to the column under 0.04. The number in that row and column is 0.4052. So, the area to the left of z = -0.24 is 0.4052, as shown in the figure at the left. 20.5 20.4 20.3 20.2 20.1 20.0 z .09 .08 .07 .06 .05 .03 23.4 23.3 23.2 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0004 .0004 .0004 .0004 .0004 .0005 .0005 .0005 .0006 .0006 .0006 .0003 .0006 .2776 .2810 .2843 .2877 .2912 .2946 .2981 .3121 .3156 .3192 .3228 .3264 .3300 .3336 .3483 .3520 .3557 .3594 .3632 .3669 .3707 .3859 .3897 .3936 .3974 .4013 .4052 .4090 .4247 .4286 .4325 .4364 .4404 .4443 .4483 .4641 .4681 .4721 .4761 .4801 .4840 .4880 .0004 .04 You can use technology to find the cumulative area that corresponds to z = -0.24, as shown at the left. Note that to specify the lower bound, use -10,000. TRY IT YOURSELF 3 1. Find the cumulative area that corresponds to a z@score of -2.19. 2. Find the cumulative area that corresponds to a z@score of 2.17. Answer: Page A39 When the z@score is not in the table, use the entry closest to it. For a z@score that is exactly midway between two z@scores, use the area midway between the corresponding areas. EXAMPLE 3 TI-84 PLUS normalcdf(-10000,-.24,0,1) 0.405165175 TI-84 PLUS normalcdf(-10000,1.15,0,1) 0.8749280114
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