Find the percentile for the observed value in the following situations: *a. Quantitative reasoning GRE score of 146 (mean = 151.3, s.d. = 8.7).

*b. Stanford-Binet IQ score of 97 (mean = 100, s.d. = 15).

c. Woman's height of 68 inches (mean = 65 inches, s.d. = 2.5 inches).

d. Man's height of 68 inches (mean = 70 inches, s.d. = 3 inches).

Please show

• Curves
• Formulas
• Values inserted into formulas
• Intermediate calculations
• Values from the Normal Probability Table below

640 APPENDICES TABLE E.2 BB18AT The Cumulative Standardized Normal Distribution Entry represents area under the cumulative standardized normal distribution from - co to Z - 0o Z Cumulative Probabilities Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -6.0 0.000000001 -5.5 0.000000019 -5.0 0.000000287 4.5 0.000003398 -4.0 0.000031671 -3.9 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003 -3.8 0.00007 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005 -3.7 0.00011 0.00010 0.00010 0.00010 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008 -3.6 0.00016 0.00015 0.00015 0.00014 0.00014 0.00013 0.00013 0.00012 0.00012 0.00011 -3.5 0.00023 0.00022 0.00022 0.00021 0.00020 0.00019 0.00019 0.00018 0.00017 0.00017 -3.4 0.00034 0.00032 0.00031 0.00030 0.00029 0.00028 0.00027 0.00026 0.00025 0.00024 3.3 0.00048 0.00047 0.00045 0.00043 0.00042 0.00040 0.00039 0.00038 0.00036 0.00035 -3.2 0.00069 0.00066 0.00064 0.00062 0.00060 0.00058 0.00056 0.00054 0.00052 0.00050 -3.1 0.00097 0.00094 0.00090 0.00087 0.00084 0.00082 0.00079 0.00076 0.00074 0.00071 3.0 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00111 0.00107 0.00103 0.00100 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 - 2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 - 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 - 2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 - 2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 - 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.090 0.0885 0.0869 0.0853 0.0838 0.0823 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 - 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.21 19 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2420 0.2388 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2482 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641TABLE E.2 The Cumulative Standardized Normal Disiribution (continued) Entry represents area under the cumulative standardized normal distribution from - [02 0.1 0.2 0.3 . 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 l .3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2. l 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.5 5.0 5.5 6.0 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.788 1 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.97 I 3 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.99865 0.99903 0.99931 0.99952 0.99966 0.99977 0.99984 0.99989 0.99993 0.99995 0.999968329 0.999996602 0999999713 0.999999981 0999999999 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7612 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0. 9345 0.9463 0.9564 0.9649 0. 9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0. 99869 0.99906 0.99934 0.99953 0.99968 0.99978 0.99985 0.99990 0.99993 0.99995 0. 5478 0. 5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.3461 0.8686 0.8888 0.9066 ..0 9222 0. 9357 0.9474 0.9573 0.9656 0.9726 0.9703 0.9330 0.9868 0.9098 - 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.99874 0.99910 0.99936 0. 99955 0.99969 0. 99978 0 99985 0.99990 0. 99993 0.99996 0.5517' 0.5910 0.6293 0.6664 0.7019 0. 7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0. 9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.99878 0.99913 0.99938 0.99957 0.99970 0.99979 0.99986 0.99990 0.99994 0.99996 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0. 7995 0. 8264 0.8508 0.8729 0.8925 0. 9099 0. 9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0. 9945 0.9959 0.9969 0. 9977 0.9984 0.99882 0.99916 0.99940 0. 99958 0. 99971 0.99980 0.99986 0.99991 0. 99994 0. 99996 05596 ' 0.5987 0.6368 0.6736 0.7000 0.7422 0.7734 0.8023 0.0209 0.0531 0.3749 0.8944 0.91 15 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9790 0.9842 0. 9070 0 9906 0 9929 0.9946 0 9960 0. 9m 0. 9970 0.9904 0.99886 0.99913 0.99942 0 99960 0. 99972 0. 99901 0.99987 0. 99991 0. 99994 0.99996 0.5636 0. 6026 0. 6406 0. 6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0. 9750 0.9803 0.9846 0. 9881 0.9909 0.9931 0.9948 0.9961 0. 9971 0. 9979 0. 9985 0.99889 0.99921 0.99944 0.99961 0.99973 0.99981 0.99987 0.99992 0.99994 0.99996 APPENDIX E Tabla 641 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.991 1 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.99893 0.99924 0.99946 0. 99962 0. 99974 0.99982 0. 99988 0.99992 0. 99995 0.99996 0.5714 0.6103 0.6480 0.6844 0.7190 0.7518 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.99897 0.99926 0.99948 0.99964 0.99975 0.99983 0.99988 0.99992 0.99995 0.99997 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0. 9952 0.9964 0. 9974 0.9981 0.9986 0.99900 0.99929 0.99950 0.99965 0.99976 0.99983 0.99989 0.99992 0.99995 0.99997