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A survey found that​ women's heights are normally distributed with mean 63.5 in and standard deviation 2.5 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?

A survey found that​ women's heights are normally distributed with mean 63.5 in and standard deviation 2.5 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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A survey found that​ women's heights are normally distributed with mean 63.5 in and standard deviation 2.5 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?
POSITIVE z Scores z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 02 .03 .04 .05 .06 .07 08 .09 0.0 5000 5040 .5120 5IG0 S199 .5239 5270 .5319 .5359 0.1 .5438 .5478 .5517 5557 .5596 .5636 .5675 5714 .5753 0.2 5795 S832 5871 5910 5948 5987 6026 6084 6141 0.3 .6179 6217 .6255 .6293 6331 .6368 .6406 .6443 6480 .6517 0.4 .6554 6591 G620 .GGG4 6700 .6736 .6772 GBOB 6844 .G879 0.5 6915 6950 6985 TORR 7123 7157 190 7224 0.6 7257 7291 7324 7357 7389 7422 7454 7486 7517 .7549 0,7 .7580 7642 7673 7704 .7734 7764 .7794 7823 ,7852 0.8 .7801 7910 7939 7967 7995 8023 B05 8078 8106 .8133 0.9 8159 8186 8212 8238 8289 B315 8340 B365 10 8413 8438 8461 B485 8508 8531 8554 .8577 A5 99 .B621 8643 B665 B686 8708 8729 8749 8770 8790 8810 .8830 1.1 1.2 8849 s869 8888 8907 8925 8944 8962 8980 8997 9015 1.3 .9032 9049 9066 .9082 9099 .915 .9131 .9147 9162 .9177 14 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 959) .9599 .9608 9616 .9625 .9633 9649 9719 18 .9541 .9656 9664 9671 9578 .9686 9693 9699 .9706 1.9 .9713 9726 .9732 9738 .9744 .9750 9756 .9761 .9767 20 .9772 9778 .9783 .9788 9793 .9798 .9803 .9808 9812 .9817 21 .9821 9826 .9830 .9834 9838 .9842 .9846 .9850 9854 .9857 22 9861 S864 9868 9871 9875 9878 9881 .9884 .9887 .9890 2.3 .9893 9896 .9898 .9901 9904 .9906 .9909 .991 .9913 9916 2.4 .9918 9920 9922 .9025 9927 .9929 .9932 9934 .9936 25 .9938 9940 9941 9043 9945 .9946 .9948 .9949 9951 .9952 26 9953 9955 .9956 9957 9959 9960 .9961 9962 9965 2.7 .9965 9966 9967 9968 9969 9970 9971 9972 9973 .9974 2.8 .9974 3975 .9976 .9977 9977 .9970 .9979 9979 9980 9381 9986 9990 29 .9981 9982 .9982 .9983 9984 9984 .9985 9985 9986 3.0 9987 9987 9987 9988 9988 9989 9989 9989 .9990 3.1 9990 9991 9991 9991 9992 9992 9992 9992 9993 9993 3.2 .9993 9993 9994 9994 9994 9994 .9994 .9995 9995 .9995 3.3 9995 9995 .9995 g996 9996 9g96 9996 9996 9996 9997 3.4 9997 9997 9997 9997 9997 9997 9997 9997 9997 9998 3.50 9999 end up NOTE. For values of z above 3.49. use 0.9999 for the area Common Cri tical Value "Use these common values that result from interpolation: Confidence | Critical Level E score Area Value 1.646 0.9500 0.90 1645 2575 0.9950 0.95 196 0.99 2.575
Transcribed Image Text:POSITIVE z Scores z Scores Standard Normal (z) Distribution: Cumulative Area from the LEFT .00 .01 02 .03 .04 .05 .06 .07 08 .09 0.0 5000 5040 .5120 5IG0 S199 .5239 5270 .5319 .5359 0.1 .5438 .5478 .5517 5557 .5596 .5636 .5675 5714 .5753 0.2 5795 S832 5871 5910 5948 5987 6026 6084 6141 0.3 .6179 6217 .6255 .6293 6331 .6368 .6406 .6443 6480 .6517 0.4 .6554 6591 G620 .GGG4 6700 .6736 .6772 GBOB 6844 .G879 0.5 6915 6950 6985 TORR 7123 7157 190 7224 0.6 7257 7291 7324 7357 7389 7422 7454 7486 7517 .7549 0,7 .7580 7642 7673 7704 .7734 7764 .7794 7823 ,7852 0.8 .7801 7910 7939 7967 7995 8023 B05 8078 8106 .8133 0.9 8159 8186 8212 8238 8289 B315 8340 B365 10 8413 8438 8461 B485 8508 8531 8554 .8577 A5 99 .B621 8643 B665 B686 8708 8729 8749 8770 8790 8810 .8830 1.1 1.2 8849 s869 8888 8907 8925 8944 8962 8980 8997 9015 1.3 .9032 9049 9066 .9082 9099 .915 .9131 .9147 9162 .9177 14 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 959) .9599 .9608 9616 .9625 .9633 9649 9719 18 .9541 .9656 9664 9671 9578 .9686 9693 9699 .9706 1.9 .9713 9726 .9732 9738 .9744 .9750 9756 .9761 .9767 20 .9772 9778 .9783 .9788 9793 .9798 .9803 .9808 9812 .9817 21 .9821 9826 .9830 .9834 9838 .9842 .9846 .9850 9854 .9857 22 9861 S864 9868 9871 9875 9878 9881 .9884 .9887 .9890 2.3 .9893 9896 .9898 .9901 9904 .9906 .9909 .991 .9913 9916 2.4 .9918 9920 9922 .9025 9927 .9929 .9932 9934 .9936 25 .9938 9940 9941 9043 9945 .9946 .9948 .9949 9951 .9952 26 9953 9955 .9956 9957 9959 9960 .9961 9962 9965 2.7 .9965 9966 9967 9968 9969 9970 9971 9972 9973 .9974 2.8 .9974 3975 .9976 .9977 9977 .9970 .9979 9979 9980 9381 9986 9990 29 .9981 9982 .9982 .9983 9984 9984 .9985 9985 9986 3.0 9987 9987 9987 9988 9988 9989 9989 9989 .9990 3.1 9990 9991 9991 9991 9992 9992 9992 9992 9993 9993 3.2 .9993 9993 9994 9994 9994 9994 .9994 .9995 9995 .9995 3.3 9995 9995 .9995 g996 9996 9g96 9996 9996 9996 9997 3.4 9997 9997 9997 9997 9997 9997 9997 9997 9997 9998 3.50 9999 end up NOTE. For values of z above 3.49. use 0.9999 for the area Common Cri tical Value "Use these common values that result from interpolation: Confidence | Critical Level E score Area Value 1.646 0.9500 0.90 1645 2575 0.9950 0.95 196 0.99 2.575
NEGATIVE z Scores Standard Normal (2) Distribution: Cumulative Area from the LEFT .00 .01 02 .03 .04 .05 .06 .07 08 .09 -3.50 and lowor .0001 .c003 .c005 -3.4 0003 0003 .0003 0003 0003 C003 0003 0002 -3.3 .0005 .000s .0004 .0004 .0004 .0004 0004 0004 .0003 -3.2 .0007 D007 0006 .0006 .0006 .0006 0006 0005 0005 0005 -31 .0010 .0009 0009 .0009 0008 0008 0008 0007 0007 -3.0 .0013 D013 O013 012 o012 .oon O010 -2.9 .0019 0018 0018 .0017 .O016 .0015 0015 .0014 .0014 0024 .0023 0023 .0021 0029 -2.8 .0026 0025 .0022 0021 .0020 .0019 -2.7 .0035 .0032 0031 .0030 0027 0026 -2.6 .0047 0045 0044 .0043 0041 .0040 0039 0057 0036 -2.5 .0062 0060 0057 .0055 0054 0052 • 0049 .0046 -2.4 .0082 .co80 0070 .0075 .0073 .0071 .0069 .00GG .0064 -2.3 .0107 0104 .0102 .0099 0096 .0094 0087 .0084 -2.2 .0139 O136 0132 0129 0125 .0122 on9 O 16 on3 .O110 -21 .0179 0174 0170 .0106 .0162 .0130 0154 .0197 0150 0146 .0143 -2.0 .0226 0222 0217 0212 .0207 .0202 O 192 .0188 .0103 -19 .0287 0281 0274 .0268 0262 .0256 .0250 0244 0239 .0233 -18 .0359 D351 .O336 0529 .0322 0514 0307 0301 0294 -17 .0446 .0436 0427 .048 0409 .0401 0392 0384 .0375 .0367 -16 .0548 .0537 0526 .0516 0465 0505 * .0495 O618 .0606 0485 0475 .0455 -15 .0668 0655 0643 .0630 .0594 OS82 0571 0550 -14 .0808 0793 0778 .D764 0749 .0735 0721 0694 OGRI -13 .0968 0951 .0934 .098 0901 0885 .o869 0853 0838 O823 -12 1151 J131 12 1093 1075 1056 1038 1020 1003 .0985 -11 1357 J335 1314 1292 1271 1251 1230 1210 1190 1170 -10 .1587 1562 15.59 1515 1492 14 69 1446 1423 1401 .1579 -0.9 1841 1814 1788 1762 1736 1711 1685 1660 1635 1611 -0.8 .2119 2090 2061 2033 2005 1977 1949 1922 1894 1867 -0.7 .2420 2309 2350 2327 2236 2266 2236 2206 2177 2140 -0.6 .2748 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 2156 3121 -0.3 5821 3/83 3745 3/07 3669 3594 3557 3520 3483 -0.2 .4207 4168 A129 4090 4062 4013 3974 3936 3897 3859 -0.1 .4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 -0.0 S000 1960 1920 A880 AB40 801 A761 AT21 A681 4641 NOTE: For values of z below -3.49, use 0.0001 for the area. "Use these common values that result from interpolation: Z score Area -1.645 0.0500 -2575 0.0050
Transcribed Image Text:NEGATIVE z Scores Standard Normal (2) Distribution: Cumulative Area from the LEFT .00 .01 02 .03 .04 .05 .06 .07 08 .09 -3.50 and lowor .0001 .c003 .c005 -3.4 0003 0003 .0003 0003 0003 C003 0003 0002 -3.3 .0005 .000s .0004 .0004 .0004 .0004 0004 0004 .0003 -3.2 .0007 D007 0006 .0006 .0006 .0006 0006 0005 0005 0005 -31 .0010 .0009 0009 .0009 0008 0008 0008 0007 0007 -3.0 .0013 D013 O013 012 o012 .oon O010 -2.9 .0019 0018 0018 .0017 .O016 .0015 0015 .0014 .0014 0024 .0023 0023 .0021 0029 -2.8 .0026 0025 .0022 0021 .0020 .0019 -2.7 .0035 .0032 0031 .0030 0027 0026 -2.6 .0047 0045 0044 .0043 0041 .0040 0039 0057 0036 -2.5 .0062 0060 0057 .0055 0054 0052 • 0049 .0046 -2.4 .0082 .co80 0070 .0075 .0073 .0071 .0069 .00GG .0064 -2.3 .0107 0104 .0102 .0099 0096 .0094 0087 .0084 -2.2 .0139 O136 0132 0129 0125 .0122 on9 O 16 on3 .O110 -21 .0179 0174 0170 .0106 .0162 .0130 0154 .0197 0150 0146 .0143 -2.0 .0226 0222 0217 0212 .0207 .0202 O 192 .0188 .0103 -19 .0287 0281 0274 .0268 0262 .0256 .0250 0244 0239 .0233 -18 .0359 D351 .O336 0529 .0322 0514 0307 0301 0294 -17 .0446 .0436 0427 .048 0409 .0401 0392 0384 .0375 .0367 -16 .0548 .0537 0526 .0516 0465 0505 * .0495 O618 .0606 0485 0475 .0455 -15 .0668 0655 0643 .0630 .0594 OS82 0571 0550 -14 .0808 0793 0778 .D764 0749 .0735 0721 0694 OGRI -13 .0968 0951 .0934 .098 0901 0885 .o869 0853 0838 O823 -12 1151 J131 12 1093 1075 1056 1038 1020 1003 .0985 -11 1357 J335 1314 1292 1271 1251 1230 1210 1190 1170 -10 .1587 1562 15.59 1515 1492 14 69 1446 1423 1401 .1579 -0.9 1841 1814 1788 1762 1736 1711 1685 1660 1635 1611 -0.8 .2119 2090 2061 2033 2005 1977 1949 1922 1894 1867 -0.7 .2420 2309 2350 2327 2236 2266 2236 2206 2177 2140 -0.6 .2748 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 2156 3121 -0.3 5821 3/83 3745 3/07 3669 3594 3557 3520 3483 -0.2 .4207 4168 A129 4090 4062 4013 3974 3936 3897 3859 -0.1 .4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 -0.0 S000 1960 1920 A880 AB40 801 A761 AT21 A681 4641 NOTE: For values of z below -3.49, use 0.0001 for the area. "Use these common values that result from interpolation: Z score Area -1.645 0.0500 -2575 0.0050
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