A random sample of size n₁ = 22, taken from a normal population with a standard deviation o₁ = 5, has a mean x₁ = 83. A second random sample of size n₂ = 33, taken from a different normal population with a standard deviation 02 = 4, has a mean x2 = 39. Find a 94% confidence interval for µ₁ – μ₂. 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 confidence interval is ☐ <μ₁₂ <☐ (Round to one decimal place as needed.) Areas under the Normal Curve Area Areas under the Normal Curve .03 .04 -1.2 -1.1 0.3015 2 .00 .01 .02 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.3 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0006 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 -3.1 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0019 0.0021 -2.8 0.0020 0.0035 0.0033 0.0031 0.0030 0.0029 -2.7 0.0027 0.0034 0.0032 0.0028 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4 -2.3 0.0107 0.0104 0.0099 0.0102 0.0091 0.0096 0.0094 0.0087 0.0089 0.0084 -2.3 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2 -2.1 0.0179 0.0166 0.0162 0.0158 0.0154 0.0150 0.0143 -2.1 0.0174 0.0170 0.0146 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0 -1.9 0.0287 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 0.0281 -1.9 0.0274 0.0359 -1.8 0.0344 0.0351 0.0336 0.0329 0.0307 0.0322 0.0301 0.0314 0.0294 -1.8 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 -1.7 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0516 0.0537 0.0465 0.0526 0.0455 -1.6 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 0.0808 0.0793 0.0764 -1.4 0.0721 0.0708 0.0778 0.0681 0.0749 -1.4 0.0735 0.0694 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 0.1131 0.1151 0.1112 0.1093 0.1056 0.1075 0.1038 0.1003 0.0985 -1.2 0.1020 0.1335 0.1314 0.1357 0.1251 0.1292 0.1271 0.1230 0.1210 0.1190 -1.1 0.1170 0.1539 0.1423 -1.0 0.1587 0.1562 0.1515 0.1492 0.1469 0.1446 0.1379 0.1401 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.2389 -0.7 0.2420 0.2266 0.2358 0.2236 0.2327 0.2296 0.2206 0.2177 -0.6 0.2743 0.2709 0.2643 0.2578 0.2546 0.2514 0.2483 0.2676 0.2611 -0.5 0.3085 0.3050 0.2946 0.2912 0.2981 0.2810 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 -0.3 0.3783 0.3745 0.3707 0.3632 0.3821 0.3669 0.3594 0.3557 0.3520 -0.2 0.4207 0.4090 0.4168 0.4129 0.4052 0.4013 0.3974 0.3936 0.3897 0.4602 0.4522 0.4483 0.4443 -0.1 0.4364 0.4562 0.4325 0.4404 0.4286 0.4960 0.4801 -0.0 0.4721 0.5000 0.4920 0.4880 0.4840 0.4761 0.4681 .00 .01 .02 .03 .04 .05 .06 .07 .08 .05 .06 .07 .08 .09 Z .00 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0.0 0.1 0.0004 0.0006 0.2 0.3 0.4 .01 .02 .03 .04 .05 .06 .07 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.6103 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6141 0.2 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6480 0.6406 0.6443 0.3 0.6517 0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 .08 .09 名 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 -2.7 0.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 0.7291 0.7324 0.7357 0.7611 0.7673 0.7642 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8508 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.9066 0.9099 1.3 0.9131 0.9032 0.9049 0.9082 0.9115 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9345 0.9357 0.9370 0.9332 0.9382 0.9394 0.9406 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 1.8 0.9656 0.9664 0.9641 0.9649 0.9671 0.9678 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.5 0.7389 0.7422 0.7454 0.7486 0.7549 0.7517 0.6 0.7794 0.7823 0.7852 0.7704 0.7 0.7734 0.7764 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 1.1 0.8810 0.8830 0.8980 0.8997 0.9015 1.2 0.9177 0.9147 0.9162 1.3 0.9292 0.9306 0.9319 1.4 0.9686 0.9750 2.0 2.1 2.2 0.9861 0.9864 0.9772 0.9783 0.9778 0.9821 0.9826 0.9830 0.9868 2.3 0.1611 -0.9 0.9893 0,9896 2.4 0.9918 0.9920 2.5 0.9938 0.9940 0.9898 0.9922 0.1894 0.1867 -0.8 0.2148 -0.7 0.2451 -0.6 0.2776 -0.5 0.3121 0.3483 0.3859 0.4247 0.4641 -0.0 .09 -0.4 -0.3 -0.2 -0.1 2 ▲ B' \' C']' σ' 2.6 0.9957 0.9927 0.9929 0.9943 0.9945 0.9946 0.9959 0.9960 0.9931 0.9429 0.9418 0.9441 1.5 0.9525 0.9535 0.9545 1.6 0.9616 0.9625 0.9633 1.7 0.9699 0.9693 0.9706 1.8 1.9 0.9756 0.9761 0.9767 0.9788 2.0 0.9798 0.9803 0.9793 0.9817 0.9808 0.9812 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9871 0.9875 0.9878 0.9881 0.9890 2.2 0.9913 0.9901 0.9904 0.9906 0.9909 0.9911 0.9925 0.9932 0.9934 0.9916 2.3 0.9936 2.4 ¡Ai --‹ ›0 = 0 2.7 2.8 2.9 3.4 2 .00 0.9941 0.9956 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9974 0.9976 0.9975 0.9977 0.9977 0.9979 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9985 0.9986 2.9 0.9984 0.9985 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9993 0.9991 0.9991 0.9992 0.9992 0.9991 0.9993 3.1 0.9992 0.9992 3.2 0.9993 3.2 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 0.9948 0.9949 0.9951 0.9952 2.5 0.9961 0.9962 0.9963 0.9964 2.6 0.9972 0.9973 0.9974 2.7 0.9979 0.9980 0.9981 2.8 0.9986 0.9997 3.3 3.4 .05 .06 .07 .08 .09
A random sample of size n₁ = 22, taken from a normal population with a standard deviation o₁ = 5, has a mean x₁ = 83. A second random sample of size n₂ = 33, taken from a different normal population with a standard deviation 02 = 4, has a mean x2 = 39. Find a 94% confidence interval for µ₁ – μ₂. 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 confidence interval is ☐ <μ₁₂ <☐ (Round to one decimal place as needed.) Areas under the Normal Curve Area Areas under the Normal Curve .03 .04 -1.2 -1.1 0.3015 2 .00 .01 .02 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.3 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.0006 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 -3.1 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0019 0.0021 -2.8 0.0020 0.0035 0.0033 0.0031 0.0030 0.0029 -2.7 0.0027 0.0034 0.0032 0.0028 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5 -2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4 -2.3 0.0107 0.0104 0.0099 0.0102 0.0091 0.0096 0.0094 0.0087 0.0089 0.0084 -2.3 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2 -2.1 0.0179 0.0166 0.0162 0.0158 0.0154 0.0150 0.0143 -2.1 0.0174 0.0170 0.0146 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0 -1.9 0.0287 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 0.0281 -1.9 0.0274 0.0359 -1.8 0.0344 0.0351 0.0336 0.0329 0.0307 0.0322 0.0301 0.0314 0.0294 -1.8 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 -1.7 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0516 0.0537 0.0465 0.0526 0.0455 -1.6 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 0.0808 0.0793 0.0764 -1.4 0.0721 0.0708 0.0778 0.0681 0.0749 -1.4 0.0735 0.0694 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 0.1131 0.1151 0.1112 0.1093 0.1056 0.1075 0.1038 0.1003 0.0985 -1.2 0.1020 0.1335 0.1314 0.1357 0.1251 0.1292 0.1271 0.1230 0.1210 0.1190 -1.1 0.1170 0.1539 0.1423 -1.0 0.1587 0.1562 0.1515 0.1492 0.1469 0.1446 0.1379 0.1401 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.2389 -0.7 0.2420 0.2266 0.2358 0.2236 0.2327 0.2296 0.2206 0.2177 -0.6 0.2743 0.2709 0.2643 0.2578 0.2546 0.2514 0.2483 0.2676 0.2611 -0.5 0.3085 0.3050 0.2946 0.2912 0.2981 0.2810 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 -0.3 0.3783 0.3745 0.3707 0.3632 0.3821 0.3669 0.3594 0.3557 0.3520 -0.2 0.4207 0.4090 0.4168 0.4129 0.4052 0.4013 0.3974 0.3936 0.3897 0.4602 0.4522 0.4483 0.4443 -0.1 0.4364 0.4562 0.4325 0.4404 0.4286 0.4960 0.4801 -0.0 0.4721 0.5000 0.4920 0.4880 0.4840 0.4761 0.4681 .00 .01 .02 .03 .04 .05 .06 .07 .08 .05 .06 .07 .08 .09 Z .00 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0.0 0.1 0.0004 0.0006 0.2 0.3 0.4 .01 .02 .03 .04 .05 .06 .07 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.6103 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6141 0.2 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6480 0.6406 0.6443 0.3 0.6517 0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 .08 .09 名 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 -2.7 0.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 0.7291 0.7324 0.7357 0.7611 0.7673 0.7642 0.7910 0.7939 0.7967 0.8186 0.8212 0.8238 0.8438 0.8461 0.8485 0.8508 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.9066 0.9099 1.3 0.9131 0.9032 0.9049 0.9082 0.9115 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9345 0.9357 0.9370 0.9332 0.9382 0.9394 0.9406 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 1.8 0.9656 0.9664 0.9641 0.9649 0.9671 0.9678 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 0.5 0.7389 0.7422 0.7454 0.7486 0.7549 0.7517 0.6 0.7794 0.7823 0.7852 0.7704 0.7 0.7734 0.7764 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 1.1 0.8810 0.8830 0.8980 0.8997 0.9015 1.2 0.9177 0.9147 0.9162 1.3 0.9292 0.9306 0.9319 1.4 0.9686 0.9750 2.0 2.1 2.2 0.9861 0.9864 0.9772 0.9783 0.9778 0.9821 0.9826 0.9830 0.9868 2.3 0.1611 -0.9 0.9893 0,9896 2.4 0.9918 0.9920 2.5 0.9938 0.9940 0.9898 0.9922 0.1894 0.1867 -0.8 0.2148 -0.7 0.2451 -0.6 0.2776 -0.5 0.3121 0.3483 0.3859 0.4247 0.4641 -0.0 .09 -0.4 -0.3 -0.2 -0.1 2 ▲ B' \' C']' σ' 2.6 0.9957 0.9927 0.9929 0.9943 0.9945 0.9946 0.9959 0.9960 0.9931 0.9429 0.9418 0.9441 1.5 0.9525 0.9535 0.9545 1.6 0.9616 0.9625 0.9633 1.7 0.9699 0.9693 0.9706 1.8 1.9 0.9756 0.9761 0.9767 0.9788 2.0 0.9798 0.9803 0.9793 0.9817 0.9808 0.9812 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9871 0.9875 0.9878 0.9881 0.9890 2.2 0.9913 0.9901 0.9904 0.9906 0.9909 0.9911 0.9925 0.9932 0.9934 0.9916 2.3 0.9936 2.4 ¡Ai --‹ ›0 = 0 2.7 2.8 2.9 3.4 2 .00 0.9941 0.9956 0.9953 0.9955 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9974 0.9976 0.9975 0.9977 0.9977 0.9979 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9985 0.9986 2.9 0.9984 0.9985 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9993 0.9991 0.9991 0.9992 0.9992 0.9991 0.9993 3.1 0.9992 0.9992 3.2 0.9993 3.2 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 0.9948 0.9949 0.9951 0.9952 2.5 0.9961 0.9962 0.9963 0.9964 2.6 0.9972 0.9973 0.9974 2.7 0.9979 0.9980 0.9981 2.8 0.9986 0.9997 3.3 3.4 .05 .06 .07 .08 .09
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:A random sample of size n₁ = 22, taken from a normal population with a standard deviation o₁ = 5, has a mean
x₁ = 83. A second random sample of size n₂ = 33, taken from a different normal population with a standard deviation
02 = 4, has a mean x2 = 39. Find a 94% confidence interval for µ₁ – μ₂.
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 confidence interval is ☐ <μ₁₂ <☐
(Round to one decimal place as needed.)
![Areas under the Normal Curve
Area
Areas under the Normal Curve
.03
.04
-1.2
-1.1
0.3015
2
.00
.01
.02
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
0.0004
0.0004 0.0004 0.0004 0.0003 -3.3
-3.2 0.0007 0.0007
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005 -3.2
0.0006
-3.1 0.0010 0.0009
0.0009
0.0009
0.0008
0.0008
0.0008
0.0008 0.0007
-3.1
0.0007
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021
0.0019
0.0021
-2.8
0.0020
0.0035
0.0033
0.0031 0.0030 0.0029
-2.7
0.0027
0.0034
0.0032
0.0028
0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5
-2.4 0.0082 0.0080
0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
-2.3 0.0107 0.0104
0.0099
0.0102
0.0091
0.0096 0.0094
0.0087
0.0089
0.0084 -2.3
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2
-2.1 0.0179
0.0166 0.0162 0.0158 0.0154 0.0150
0.0143 -2.1
0.0174 0.0170
0.0146
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9 0.0287
0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
0.0281
-1.9
0.0274
0.0359
-1.8
0.0344
0.0351
0.0336 0.0329
0.0307
0.0322
0.0301
0.0314
0.0294 -1.8
0.0446 0.0436 0.0427 0.0418 0.0409 0.0401
-1.7
0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548
0.0516
0.0537
0.0465
0.0526
0.0455 -1.6
0.0505 0.0495 0.0485 0.0475
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
0.0808 0.0793
0.0764
-1.4
0.0721 0.0708
0.0778
0.0681
0.0749
-1.4
0.0735
0.0694
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
0.1131
0.1151
0.1112 0.1093
0.1056
0.1075
0.1038
0.1003 0.0985 -1.2
0.1020
0.1335 0.1314
0.1357
0.1251
0.1292 0.1271
0.1230 0.1210 0.1190
-1.1
0.1170
0.1539
0.1423
-1.0 0.1587 0.1562
0.1515 0.1492 0.1469 0.1446
0.1379
0.1401
-1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922
0.2389
-0.7 0.2420
0.2266
0.2358
0.2236
0.2327 0.2296
0.2206 0.2177
-0.6 0.2743 0.2709
0.2643
0.2578 0.2546 0.2514 0.2483
0.2676
0.2611
-0.5 0.3085 0.3050
0.2946 0.2912
0.2981
0.2810
0.2877 0.2843
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156
-0.3
0.3783 0.3745 0.3707
0.3632
0.3821
0.3669
0.3594 0.3557 0.3520
-0.2 0.4207
0.4090
0.4168 0.4129
0.4052 0.4013 0.3974 0.3936 0.3897
0.4602
0.4522 0.4483 0.4443
-0.1
0.4364
0.4562
0.4325
0.4404
0.4286
0.4960
0.4801
-0.0
0.4721
0.5000
0.4920 0.4880 0.4840
0.4761
0.4681
.00
.01
.02
.03
.04
.05
.06
.07
.08
.05
.06
.07
.08
.09
Z
.00
0.0003
0.0003 0.0003
0.0003 0.0002 -3.4
0.0
0.1
0.0004
0.0006
0.2
0.3
0.4
.01
.02
.03
.04
.05
.06
.07
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.6103
0.5793
0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064
0.6141 0.2
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368
0.6480
0.6406 0.6443
0.3
0.6517
0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
.08
.09
名
0.5
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6
-2.7
0.7
0.7257
0.7580
0.8
0.7881
0.9 0.8159
1.0 0.8413
0.9726
0.7291 0.7324 0.7357
0.7611
0.7673
0.7642
0.7910 0.7939 0.7967
0.8186 0.8212 0.8238
0.8438
0.8461 0.8485 0.8508
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962
0.9066
0.9099
1.3
0.9131
0.9032 0.9049
0.9082
0.9115
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279
1.5
0.9345 0.9357 0.9370
0.9332
0.9382 0.9394 0.9406
0.9463
0.9505
1.6
0.9515
0.9452
0.9474 0.9484 0.9495
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608
1.8
0.9656 0.9664
0.9641 0.9649
0.9671 0.9678
1.9 0.9713 0.9719
0.9732 0.9738 0.9744
0.5
0.7389 0.7422 0.7454 0.7486
0.7549
0.7517
0.6
0.7794 0.7823 0.7852
0.7704
0.7
0.7734 0.7764
0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8790
1.1
0.8810 0.8830
0.8980 0.8997 0.9015 1.2
0.9177
0.9147 0.9162
1.3
0.9292 0.9306 0.9319 1.4
0.9686
0.9750
2.0
2.1
2.2
0.9861 0.9864
0.9772
0.9783
0.9778
0.9821 0.9826 0.9830
0.9868
2.3
0.1611 -0.9
0.9893 0,9896
2.4 0.9918 0.9920
2.5 0.9938 0.9940
0.9898
0.9922
0.1894
0.1867 -0.8
0.2148 -0.7
0.2451
-0.6
0.2776 -0.5
0.3121
0.3483
0.3859
0.4247
0.4641 -0.0
.09
-0.4
-0.3
-0.2
-0.1
2
▲ B' \' C']' σ'
2.6
0.9957
0.9927 0.9929
0.9943 0.9945 0.9946
0.9959 0.9960
0.9931
0.9429
0.9418
0.9441 1.5
0.9525 0.9535 0.9545 1.6
0.9616 0.9625 0.9633 1.7
0.9699
0.9693
0.9706 1.8
1.9
0.9756 0.9761 0.9767
0.9788
2.0
0.9798 0.9803
0.9793
0.9817
0.9808 0.9812
0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
0.9884 0.9887
0.9871 0.9875 0.9878 0.9881
0.9890 2.2
0.9913
0.9901 0.9904 0.9906 0.9909 0.9911
0.9925
0.9932 0.9934
0.9916
2.3
0.9936
2.4
¡Ai
--‹ ›0 = 0
2.7
2.8
2.9
3.4
2
.00
0.9941
0.9956
0.9953
0.9955
0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971
0.9974
0.9976
0.9975
0.9977 0.9977
0.9979
0.9978
0.9981 0.9982 0.9982 0.9983 0.9984
0.9985
0.9986 2.9
0.9984
0.9985
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990
0.9993
0.9991 0.9991 0.9992 0.9992
0.9991
0.9993
3.1
0.9992 0.9992
3.2 0.9993
3.2
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
0.9995
0.9995
3.3
0.9995
0.9996
0.9996
0.9996
0.9996
0.9996
0.9997
0.9996
0.9997 0.9997 0.9997 0.9997 0.9997
0.9997
0.9997
0.9997 0.9998
.01
.02
.03
.04
0.9948
0.9949
0.9951
0.9952
2.5
0.9961
0.9962
0.9963 0.9964
2.6
0.9972
0.9973 0.9974 2.7
0.9979
0.9980
0.9981 2.8
0.9986
0.9997
3.3
3.4
.05
.06
.07
.08
.09](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1bdf417-f458-4023-ae51-f07979d4022f%2F938941dc-307b-4bd7-b884-7e226f2f96ac%2Fqn63au8_processed.png&w=3840&q=75)
Transcribed Image Text:Areas under the Normal Curve
Area
Areas under the Normal Curve
.03
.04
-1.2
-1.1
0.3015
2
.00
.01
.02
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
0.0004
0.0004 0.0004 0.0004 0.0003 -3.3
-3.2 0.0007 0.0007
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005 -3.2
0.0006
-3.1 0.0010 0.0009
0.0009
0.0009
0.0008
0.0008
0.0008
0.0008 0.0007
-3.1
0.0007
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021
0.0019
0.0021
-2.8
0.0020
0.0035
0.0033
0.0031 0.0030 0.0029
-2.7
0.0027
0.0034
0.0032
0.0028
0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5
-2.4 0.0082 0.0080
0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
-2.3 0.0107 0.0104
0.0099
0.0102
0.0091
0.0096 0.0094
0.0087
0.0089
0.0084 -2.3
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2
-2.1 0.0179
0.0166 0.0162 0.0158 0.0154 0.0150
0.0143 -2.1
0.0174 0.0170
0.0146
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9 0.0287
0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
0.0281
-1.9
0.0274
0.0359
-1.8
0.0344
0.0351
0.0336 0.0329
0.0307
0.0322
0.0301
0.0314
0.0294 -1.8
0.0446 0.0436 0.0427 0.0418 0.0409 0.0401
-1.7
0.0392 0.0384 0.0375 0.0367 -1.7
-1.6 0.0548
0.0516
0.0537
0.0465
0.0526
0.0455 -1.6
0.0505 0.0495 0.0485 0.0475
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
0.0808 0.0793
0.0764
-1.4
0.0721 0.0708
0.0778
0.0681
0.0749
-1.4
0.0735
0.0694
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3
0.1131
0.1151
0.1112 0.1093
0.1056
0.1075
0.1038
0.1003 0.0985 -1.2
0.1020
0.1335 0.1314
0.1357
0.1251
0.1292 0.1271
0.1230 0.1210 0.1190
-1.1
0.1170
0.1539
0.1423
-1.0 0.1587 0.1562
0.1515 0.1492 0.1469 0.1446
0.1379
0.1401
-1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922
0.2389
-0.7 0.2420
0.2266
0.2358
0.2236
0.2327 0.2296
0.2206 0.2177
-0.6 0.2743 0.2709
0.2643
0.2578 0.2546 0.2514 0.2483
0.2676
0.2611
-0.5 0.3085 0.3050
0.2946 0.2912
0.2981
0.2810
0.2877 0.2843
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156
-0.3
0.3783 0.3745 0.3707
0.3632
0.3821
0.3669
0.3594 0.3557 0.3520
-0.2 0.4207
0.4090
0.4168 0.4129
0.4052 0.4013 0.3974 0.3936 0.3897
0.4602
0.4522 0.4483 0.4443
-0.1
0.4364
0.4562
0.4325
0.4404
0.4286
0.4960
0.4801
-0.0
0.4721
0.5000
0.4920 0.4880 0.4840
0.4761
0.4681
.00
.01
.02
.03
.04
.05
.06
.07
.08
.05
.06
.07
.08
.09
Z
.00
0.0003
0.0003 0.0003
0.0003 0.0002 -3.4
0.0
0.1
0.0004
0.0006
0.2
0.3
0.4
.01
.02
.03
.04
.05
.06
.07
0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.6103
0.5793
0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064
0.6141 0.2
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368
0.6480
0.6406 0.6443
0.3
0.6517
0,6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
.08
.09
名
0.5
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6
-2.7
0.7
0.7257
0.7580
0.8
0.7881
0.9 0.8159
1.0 0.8413
0.9726
0.7291 0.7324 0.7357
0.7611
0.7673
0.7642
0.7910 0.7939 0.7967
0.8186 0.8212 0.8238
0.8438
0.8461 0.8485 0.8508
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962
0.9066
0.9099
1.3
0.9131
0.9032 0.9049
0.9082
0.9115
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279
1.5
0.9345 0.9357 0.9370
0.9332
0.9382 0.9394 0.9406
0.9463
0.9505
1.6
0.9515
0.9452
0.9474 0.9484 0.9495
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608
1.8
0.9656 0.9664
0.9641 0.9649
0.9671 0.9678
1.9 0.9713 0.9719
0.9732 0.9738 0.9744
0.5
0.7389 0.7422 0.7454 0.7486
0.7549
0.7517
0.6
0.7794 0.7823 0.7852
0.7704
0.7
0.7734 0.7764
0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8790
1.1
0.8810 0.8830
0.8980 0.8997 0.9015 1.2
0.9177
0.9147 0.9162
1.3
0.9292 0.9306 0.9319 1.4
0.9686
0.9750
2.0
2.1
2.2
0.9861 0.9864
0.9772
0.9783
0.9778
0.9821 0.9826 0.9830
0.9868
2.3
0.1611 -0.9
0.9893 0,9896
2.4 0.9918 0.9920
2.5 0.9938 0.9940
0.9898
0.9922
0.1894
0.1867 -0.8
0.2148 -0.7
0.2451
-0.6
0.2776 -0.5
0.3121
0.3483
0.3859
0.4247
0.4641 -0.0
.09
-0.4
-0.3
-0.2
-0.1
2
▲ B' \' C']' σ'
2.6
0.9957
0.9927 0.9929
0.9943 0.9945 0.9946
0.9959 0.9960
0.9931
0.9429
0.9418
0.9441 1.5
0.9525 0.9535 0.9545 1.6
0.9616 0.9625 0.9633 1.7
0.9699
0.9693
0.9706 1.8
1.9
0.9756 0.9761 0.9767
0.9788
2.0
0.9798 0.9803
0.9793
0.9817
0.9808 0.9812
0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
0.9884 0.9887
0.9871 0.9875 0.9878 0.9881
0.9890 2.2
0.9913
0.9901 0.9904 0.9906 0.9909 0.9911
0.9925
0.9932 0.9934
0.9916
2.3
0.9936
2.4
¡Ai
--‹ ›0 = 0
2.7
2.8
2.9
3.4
2
.00
0.9941
0.9956
0.9953
0.9955
0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971
0.9974
0.9976
0.9975
0.9977 0.9977
0.9979
0.9978
0.9981 0.9982 0.9982 0.9983 0.9984
0.9985
0.9986 2.9
0.9984
0.9985
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990
0.9993
0.9991 0.9991 0.9992 0.9992
0.9991
0.9993
3.1
0.9992 0.9992
3.2 0.9993
3.2
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
0.9995
0.9995
3.3
0.9995
0.9996
0.9996
0.9996
0.9996
0.9996
0.9997
0.9996
0.9997 0.9997 0.9997 0.9997 0.9997
0.9997
0.9997
0.9997 0.9998
.01
.02
.03
.04
0.9948
0.9949
0.9951
0.9952
2.5
0.9961
0.9962
0.9963 0.9964
2.6
0.9972
0.9973 0.9974 2.7
0.9979
0.9980
0.9981 2.8
0.9986
0.9997
3.3
3.4
.05
.06
.07
.08
.09
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