Areas under the Normal Curve 國 口≡ Z z .02 .04 0.0003 0.0004 0.0006 0.0043 0.0041 0.0057 0.0055 0.0075 0.0073 .00 .01 .03 -3.4 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 -2.6 0.0047 0.0045 0.0044 0.0040 0.0039 -2.5 0.0062 0.0060 0.0059 0.0054 0.0052 -2.4 0.0082 0.0080 0.0078 0.0071 0.0069 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 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 .05 .06 0.0003 0.0003 0.0004 0.0004 .07 .08 .09 0.0003 0.0003 0.0002 0.0015 0.0014 0.0014 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 0.0038 0.0037 0.0036 0.0051 0.0049 0.0048 0.0068 0.0066 0.0064 0.0089 0.0087 0.0084 0.0116 0.0113 0.0110 0.0150 0.0146 0.0143 0.0192 0.0188 0.0183 0.0244 0.0239 0.0233 0.0307 0.0301 0.0294 0.0384 0.0375 0.0367 0.0475 0.0465 0.0455 0.0582 0.0571 0.0559 1.1 0.0708 0.0694 0.0681 2.1 2.2 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 k -0.8 0.2119 0.2090 0.2061 -0.7 0.2420 0.2389 0.2358 -0.6 0.2743 0.2709 0.2676 -0.5 0.3085 0.3050 0.1190 0.1170 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 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 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4286 0.4247 0.4681 0.4641 B'C' + E Areas under the Normal Curve .06 .07 .08 0.5239 0.5279 0.5319 0.5359 0.5636 0.5675 0.5714 0.5753 0.6064 0.6103 0.6141 .09 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8907 0.8925 0.8944 0.8962 .00 .01 .02 .03 .04 .05 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 2.4 0.9918 2.5 0.9938 2.6 3.3 3.4 A UCLA researcher claims that the life span of mice can be extended by as much as 25% when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diet is enriched to normal levels by vitamins and protein. Assuming that it is known from previous studies that σ = 5.6 months, how many mice should be included in the sample if we wish to be 99% confident that the mean life span of the sample will be within 2 months of the population mean for all mice subjected to this reduced diet? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The required sample size is 53 (Round up to the nearest whole number as needed.)
Areas under the Normal Curve 國 口≡ Z z .02 .04 0.0003 0.0004 0.0006 0.0043 0.0041 0.0057 0.0055 0.0075 0.0073 .00 .01 .03 -3.4 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 -2.6 0.0047 0.0045 0.0044 0.0040 0.0039 -2.5 0.0062 0.0060 0.0059 0.0054 0.0052 -2.4 0.0082 0.0080 0.0078 0.0071 0.0069 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 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 .05 .06 0.0003 0.0003 0.0004 0.0004 .07 .08 .09 0.0003 0.0003 0.0002 0.0015 0.0014 0.0014 0.0021 0.0020 0.0019 0.0028 0.0027 0.0026 0.0038 0.0037 0.0036 0.0051 0.0049 0.0048 0.0068 0.0066 0.0064 0.0089 0.0087 0.0084 0.0116 0.0113 0.0110 0.0150 0.0146 0.0143 0.0192 0.0188 0.0183 0.0244 0.0239 0.0233 0.0307 0.0301 0.0294 0.0384 0.0375 0.0367 0.0475 0.0465 0.0455 0.0582 0.0571 0.0559 1.1 0.0708 0.0694 0.0681 2.1 2.2 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 k -0.8 0.2119 0.2090 0.2061 -0.7 0.2420 0.2389 0.2358 -0.6 0.2743 0.2709 0.2676 -0.5 0.3085 0.3050 0.1190 0.1170 0.1379 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 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 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4286 0.4247 0.4681 0.4641 B'C' + E Areas under the Normal Curve .06 .07 .08 0.5239 0.5279 0.5319 0.5359 0.5636 0.5675 0.5714 0.5753 0.6064 0.6103 0.6141 .09 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8907 0.8925 0.8944 0.8962 .00 .01 .02 .03 .04 .05 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 2.4 0.9918 2.5 0.9938 2.6 3.3 3.4 A UCLA researcher claims that the life span of mice can be extended by as much as 25% when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diet is enriched to normal levels by vitamins and protein. Assuming that it is known from previous studies that σ = 5.6 months, how many mice should be included in the sample if we wish to be 99% confident that the mean life span of the sample will be within 2 months of the population mean for all mice subjected to this reduced diet? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The required sample size is 53 (Round up to the nearest whole number as needed.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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