A survey found that women's heights are normally distributed with mean 63.9 in and standard deviation 2.3 in. A branch of the military requires women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements? Click to view page 1 of the table. Click to view page 2 of the table. a. The percentage of women who meet the height requirement is%. (Round to two decimal places as needed.) X Standard Normal Table (Page 1) Standard Normal (z) Distribution: Cumulative Area from the LEFT .01 02 .03 .04 .05 .06 .07 .08 09 -3.50 and lower .0001 -5.4 0003 0003 0003 0003 .0003 0003 0003 .0003 .0003 .0002 -3.3 OO! 000 0004 000 000 000 0004 .000 -3.2 3007 0007 000 0006 0006 0006 DO05 0005 -3.1 2010 0009 0009 3009 1008 0008 0008 007 0007 -3.0 ,0013 0013 0013 .0012 .D012 .0011 .oof ,0011 0910 ,0910 -2.9 .0019 0018 0018 0017 0016 .0016 0015 0015 0014 .0014 -2.8 0026 0025 .0024 0023 .0023 002 0021 0021 .0020 0019 .0035 0034 0033 0032 0029 0028 0027 0026 -2.6 .0047 0045 ,0044 ,0043 104 304 0038 0037 DO36 2.5 .0062 0060 0059 .0057 .0055 .0054 .0052 .0051 0049 .0048 -2.4 .0082 0078 0075 0 073 0071 0069 0068 .006E .0.064 .2.3 .0107 0104 0102 0099 0096 009 009 0089 008. .008 -2.2 .0139 0136 0132 0129 0125 0122 0119 0116 0113 0110 017 0174 170 0166 0162 .0158 0154 .0150 0146 0143 -2.0 .0228 0222 0217 .0212 0207 .0202 _0197 0192 .0188 0183 -1.9 .0287 0281 0274 0268 0262 0256 0250 0244 .0239 0233 -18 .0359 0351 0344 0336 0329 0322 0314 030 030 029 -17 0446 .0436 042 0418 .0409 040 0392 038 0375 0367 .0548 0537 0526 0516 0505 .0495 1485 0475 0465 .0455 .0668 .0655 0643 .0630 0618 .0606 0594 .0582 0571 .0559 -1.4 .0808 079 0778 0764 0749 0735 0721 070 0694 0681 -1 7 .0968 0951 0934 0918 0901 088 086 085 083 082 -13 1151 1131 112 1093 1075 1056 1038 1020 1003 098 -11 .1357 .1335 1314 1292 1271 1251 1230 1210 1190 1170 -1.0 1587 1562 1539 1515 1492 1469 1446 .1423 1401 1379 -0.9 184 1814 1788 1762 1736 1711 1685 1660 1635 1611 -0.8 2119 2090 2061 2033 2005 1977 1949 927 1894 1867 -0.7 .2420 2389 2358 2327 2296 2266 2236 220 2177 2148 -0.6 2743 2709 2676 643 -2617 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 348 -0.2 ,4207 4168 4129 4090 4052 4013 3974 3936 3897 3859 .4602 .4562 4522 .4183 4443 .4404 4364 .4325 4286 42475000 5279 5319 5359 0.0 5040 5080 5120 5160 5199 5239 .5398 5438 5478 5517 5557 5596 .5636 5675 5714 5753 0.1 0.2 5793 5832 5871 5910 .5948 5987 6026 6064 .6103 6141 0.3 6179 6217 6255 6293 6331 6368 6406 6443 6480 6517 6591 6628 6664 6700 6736 6772 6808 6844 6875 0.4 6554 0,5 6915 6950 6985 7019 .7054 7088 7123 7157 7190 7224 7517 0.6 ,7257 7291 7324 7357 7389 7422 ,7454 7486 .7580 7611 .7642 7673 7704 7734 7764 7794 7823 .7852 0.7 0.8 .7881 7910 7939 7967 7995 8023 .8051 8078 .8106 8133 0.9 .8159 .8186 8212 8238 8264 8289 8315 .8340 8365 .8389 1.0 .8413 8438 8461 8485 .8508 8531 8554 .8577 8599 .862 1.1 .8643 8665 8686 8708 8729 3749 8770 8790 8810 8830 1.2 8849 8869 8888 8907 3925 8944 .8962 8980 8997 9015 1.3 .9032 9049 9066 9082 9099 9115 9131 .9147 9162 917 1.4 9192 9207 9222 9236 9251 9265 .9279 9292 9306 .9319 1.5 9332 9345 9357 9370 9382 9394 9406 9418 9429 9441 1.6 9452 9463 9474 9484 9495 9505 .9515 9525 .9535 9545 1.7 .9554 .9564 .9573 9582 9591 .9599 .9608 9616 .9625 .9633 .9641 .9649 .9656 .9664 .9671 .9678 .9686 9693 9699 9706 1.8 .9713 .9719 9726 9732 9738 9744 9750 9756 9761 9767 1.9 2.0 .9772 .9778 9783 9788 .9793 9798 9803 9808 .9812 9817 2.1 .9821 .9826 9830 9834 9838 .9842 9846 9850 9854 9857 9890 2.2 9861 9864 9868 9871 9875 9878 9881 9884 9887 2.3 9893 9896 9898 9901 9904 9906 9909 9911 9913 9916 2.4 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936 2.5 9938 9940 9941 9943 9945 9946 9948 9949 .9951 9952 2.6 9953 9955 9956 9957 9959 9960 9961 9962 9963 9964 2.7 9965 .9966 9967 9968 9969 9970 9971 9972 9973 9974 2.8 .9974 .9975 .9976 9977 9977 9978 9979 9979 9980 9981 2.9 9981 9982 9982 9983 9984 9984 9985 9985 9986 9986 30 9987 9987 9987 9988 9988 9989 9989 9989 9990 9990 1993 9993 3.1 .9990 2991 2991 3991 9992 9992 9992 9992 9993 9993 9994 9994 9994 2994 9994 9995 9995 9995 3.2 3 3 9995 9995 9995 9996 9996 9996 9996 9996 9996 9997 .9997 9998 34 9997 9997 9997 9997 9997 9997 9997 9997 350 9999 and up NOTE: For values of z above 3.49, use 0.9999 for the area. Common Critical Value "Use these common values that result from interpolation: Confidence | Critical Level Value z score Area .645 1.645 0.9500 0.90 0.95 1.96 2.575 0,9950 0.99 2.575