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The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is (Round to two decimal places as needed.) %. Standard Normal Area Standard Normal Area Probabilities Probabilities (Cumulative z curve areas) (Cumulative z curve areas) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.5080 0.5120 0.5160 0.5557 0.5948 0.5199 0.5239 0.5279 0.5319 0.5359 0.0003 0.1 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.5398 0.5438 0.5478 0.5636 0.6026 b.6406 0.5517 0.5596 0.5675 0.5714 0.5753 -3.3 0.0005 0.0005 0.0005 0.2 0.5793 0.5832 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.5871 0.5910 0.5987 0.6064 0.6103 0.6141 -3.2 0.0007 0.0007 0.0006 0.3 0.6179 0.6293 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.6217 0.6255 0.6331 0.6368 0.6443 0.6480 0.6517 -3.1 0.0010 0.0009 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.6736 0.6808 0.6844 0.6879 -3.0 0.0013 0.0013 0.6915 0.6950 0.7291 0.5 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.7224 0.6 0.7257 0.7324 0.7357 0.7389 0.7422 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.0030 0.0029 0.0028 0.0027 0.0026 0.7704 0.7995 0.7642 0.7673 0.7734 0.7764 0.7794 0.7823 0.7852 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.8 0.7881 0.7910 0.7939 0.7967 0.8023 0.8051 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 0.8078 -2.6 0.0047 0.8106 0.8365 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0.8340 0.8389 -2.5 0.0062 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.0244 0.0239 0.0233 0.9406 0.9418 0.9525 0.9394 0.9429 0.9441 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.9463 0.9474 0.9484 0.9495 0.9505 0.0351 0.0436 1.6 0.9452 0.9515 0.9535 0.9545 -1.8 0.0359 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.7 0.9554 0.9564 0.9573 0.9582 0.0427 0.0526 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 -1.7 0.0446 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 -1.6 0.0548 0.0537 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 0.9726 0.0606 0.0594 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0582 0.0571 0.0559 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9817 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 0.9812 -1.4 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9929 0.9909 0.9911 0.9913 0.9916 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9931 0.9932 0.9934 0.9936 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.1685 0.9949 0.9962 0.9951 0.9952 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1660 0.1635 0.1611 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.1922 0.1867 0.9963 0.9964 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1894 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.2676 0.3015 0.9979 0.9980 0.9981 -0.6 0.2743 0.2709 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.3085 0.3050 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.3409 0.3300 0.3228 0.3156 0.9990 0.9990 -0.4 0.3446 0.3372 0.3336 0.3264 0.3192 0.3121 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.3783 0.3632 0.3594 0.3557 0.3520 0.3483 0.9993 -0.3 0.3821 0.3745 0.3707 0.3669 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 -0.2 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.4207 0.4168 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.4325 0.4286 0.9996 0.9996 0.9997 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4247 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.4801 0.4761 0.4641 0.9997 0.9998 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4721 0.4681

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is (Round to two decimal places as needed.) %. Standard Normal Area Standard Normal Area Probabilities Probabilities (Cumulative z curve areas) (Cumulative z curve areas) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.5080 0.5120 0.5160 0.5557 0.5948 0.5199 0.5239 0.5279 0.5319 0.5359 0.0003 0.1 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.5398 0.5438 0.5478 0.5636 0.6026 b.6406 0.5517 0.5596 0.5675 0.5714 0.5753 -3.3 0.0005 0.0005 0.0005 0.2 0.5793 0.5832 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.5871 0.5910 0.5987 0.6064 0.6103 0.6141 -3.2 0.0007 0.0007 0.0006 0.3 0.6179 0.6293 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.6217 0.6255 0.6331 0.6368 0.6443 0.6480 0.6517 -3.1 0.0010 0.0009 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.6736 0.6808 0.6844 0.6879 -3.0 0.0013 0.0013 0.6915 0.6950 0.7291 0.5 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.7224 0.6 0.7257 0.7324 0.7357 0.7389 0.7422 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.0030 0.0029 0.0028 0.0027 0.0026 0.7704 0.7995 0.7642 0.7673 0.7734 0.7764 0.7794 0.7823 0.7852 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.8 0.7881 0.7910 0.7939 0.7967 0.8023 0.8051 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 0.8078 -2.6 0.0047 0.8106 0.8365 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0.8340 0.8389 -2.5 0.0062 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.0244 0.0239 0.0233 0.9406 0.9418 0.9525 0.9394 0.9429 0.9441 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.9463 0.9474 0.9484 0.9495 0.9505 0.0351 0.0436 1.6 0.9452 0.9515 0.9535 0.9545 -1.8 0.0359 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.7 0.9554 0.9564 0.9573 0.9582 0.0427 0.0526 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 -1.7 0.0446 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 -1.6 0.0548 0.0537 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 0.9726 0.0606 0.0594 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0582 0.0571 0.0559 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9817 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 0.9812 -1.4 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9929 0.9909 0.9911 0.9913 0.9916 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9931 0.9932 0.9934 0.9936 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.1685 0.9949 0.9962 0.9951 0.9952 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1660 0.1635 0.1611 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.1922 0.1867 0.9963 0.9964 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1894 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.2676 0.3015 0.9979 0.9980 0.9981 -0.6 0.2743 0.2709 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.3085 0.3050 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.3409 0.3300 0.3228 0.3156 0.9990 0.9990 -0.4 0.3446 0.3372 0.3336 0.3264 0.3192 0.3121 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.3783 0.3632 0.3594 0.3557 0.3520 0.3483 0.9993 -0.3 0.3821 0.3745 0.3707 0.3669 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 -0.2 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.4207 0.4168 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.4325 0.4286 0.9996 0.9996 0.9997 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4247 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.4801 0.4761 0.4641 0.9997 0.9998 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4721 0.4681

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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The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is (Round to two decimal places as needed.) %.
Transcribed Image Text:The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 3 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service half-price? (b) If the automotive center does not want to give the discount to more than 5% of its customers, how long should it make the guaranteed time limit? (a) The percent of customers that receive the service for half-price is (Round to two decimal places as needed.) %.
Standard Normal Area Standard Normal Area Probabilities Probabilities (Cumulative z curve areas) (Cumulative z curve areas) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.5080 0.5120 0.5160 0.5557 0.5948 0.5199 0.5239 0.5279 0.5319 0.5359 0.0003 0.1 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.5398 0.5438 0.5478 0.5636 0.6026 b.6406 0.5517 0.5596 0.5675 0.5714 0.5753 -3.3 0.0005 0.0005 0.0005 0.2 0.5793 0.5832 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.5871 0.5910 0.5987 0.6064 0.6103 0.6141 -3.2 0.0007 0.0007 0.0006 0.3 0.6179 0.6293 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.6217 0.6255 0.6331 0.6368 0.6443 0.6480 0.6517 -3.1 0.0010 0.0009 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.6736 0.6808 0.6844 0.6879 -3.0 0.0013 0.0013 0.6915 0.6950 0.7291 0.5 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.7224 0.6 0.7257 0.7324 0.7357 0.7389 0.7422 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.0030 0.0029 0.0028 0.0027 0.0026 0.7704 0.7995 0.7642 0.7673 0.7734 0.7764 0.7794 0.7823 0.7852 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.8 0.7881 0.7910 0.7939 0.7967 0.8023 0.8051 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 0.8078 -2.6 0.0047 0.8106 0.8365 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0.8340 0.8389 -2.5 0.0062 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.0244 0.0239 0.0233 0.9406 0.9418 0.9525 0.9394 0.9429 0.9441 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.9463 0.9474 0.9484 0.9495 0.9505 0.0351 0.0436 1.6 0.9452 0.9515 0.9535 0.9545 -1.8 0.0359 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.7 0.9554 0.9564 0.9573 0.9582 0.0427 0.0526 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 -1.7 0.0446 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 -1.6 0.0548 0.0537 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 0.9726 0.0606 0.0594 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0582 0.0571 0.0559 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9817 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 0.9812 -1.4 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9929 0.9909 0.9911 0.9913 0.9916 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9931 0.9932 0.9934 0.9936 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.1685 0.9949 0.9962 0.9951 0.9952 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1660 0.1635 0.1611 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.1922 0.1867 0.9963 0.9964 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1894 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.2676 0.3015 0.9979 0.9980 0.9981 -0.6 0.2743 0.2709 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.3085 0.3050 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.3409 0.3300 0.3228 0.3156 0.9990 0.9990 -0.4 0.3446 0.3372 0.3336 0.3264 0.3192 0.3121 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.3783 0.3632 0.3594 0.3557 0.3520 0.3483 0.9993 -0.3 0.3821 0.3745 0.3707 0.3669 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 -0.2 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.4207 0.4168 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.4325 0.4286 0.9996 0.9996 0.9997 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4247 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.4801 0.4761 0.4641 0.9997 0.9998 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4721 0.4681
Transcribed Image Text:Standard Normal Area Standard Normal Area Probabilities Probabilities (Cumulative z curve areas) (Cumulative z curve areas) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.5080 0.5120 0.5160 0.5557 0.5948 0.5199 0.5239 0.5279 0.5319 0.5359 0.0003 0.1 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 0.5398 0.5438 0.5478 0.5636 0.6026 b.6406 0.5517 0.5596 0.5675 0.5714 0.5753 -3.3 0.0005 0.0005 0.0005 0.2 0.5793 0.5832 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.5871 0.5910 0.5987 0.6064 0.6103 0.6141 -3.2 0.0007 0.0007 0.0006 0.3 0.6179 0.6293 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.6217 0.6255 0.6331 0.6368 0.6443 0.6480 0.6517 -3.1 0.0010 0.0009 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6772 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 0.6736 0.6808 0.6844 0.6879 -3.0 0.0013 0.0013 0.6915 0.6950 0.7291 0.5 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.7224 0.6 0.7257 0.7324 0.7357 0.7389 0.7422 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.0030 0.0029 0.0028 0.0027 0.0026 0.7704 0.7995 0.7642 0.7673 0.7734 0.7764 0.7794 0.7823 0.7852 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.8 0.7881 0.7910 0.7939 0.7967 0.8023 0.8051 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 0.8078 -2.6 0.0047 0.8106 0.8365 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 0.8340 0.8389 -2.5 0.0062 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.0244 0.0239 0.0233 0.9406 0.9418 0.9525 0.9394 0.9429 0.9441 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.9463 0.9474 0.9484 0.9495 0.9505 0.0351 0.0436 1.6 0.9452 0.9515 0.9535 0.9545 -1.8 0.0359 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1.7 0.9554 0.9564 0.9573 0.9582 0.0427 0.0526 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 -1.7 0.0446 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 -1.6 0.0548 0.0537 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 0.9726 0.0606 0.0594 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0582 0.0571 0.0559 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9817 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 0.9812 -1.4 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9929 0.9909 0.9911 0.9913 0.9916 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9931 0.9932 0.9934 0.9936 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.1685 0.9949 0.9962 0.9951 0.9952 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1660 0.1635 0.1611 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.1922 0.1867 0.9963 0.9964 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1894 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.2676 0.3015 0.9979 0.9980 0.9981 -0.6 0.2743 0.2709 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 0.3085 0.3050 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.3409 0.3300 0.3228 0.3156 0.9990 0.9990 -0.4 0.3446 0.3372 0.3336 0.3264 0.3192 0.3121 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.3783 0.3632 0.3594 0.3557 0.3520 0.3483 0.9993 -0.3 0.3821 0.3745 0.3707 0.3669 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 -0.2 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 0.4207 0.4168 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.4325 0.4286 0.9996 0.9996 0.9997 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4247 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.4801 0.4761 0.4641 0.9997 0.9998 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4721 0.4681
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