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 0.7 -2.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 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 0.7291 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 0.9429 0.9382 0.9394 0.9406 0.9441 1.5 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9656 0.9699 0.9664 0.9641 0.9649 0.9693 0.9706 0.9671 1.8 0.9678 1.9 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 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 0.5 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 0.9418 0.9686 0.9750 0.9756 0.9916 2.3 0.9931 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 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 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 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 .08 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 0.9996 0.9997 3.3 3.4 .05 .06 .07 .09 The burn time for the first stage of a rocket is a normal random variable with a standard deviation of 0.8 minute. Assume a normal prior distribution for μ with a mean of 10 minutes and a standard deviation of 0.3 minute. If 12 of these rockets are fired and the first stage has an average burn time of 11 minutes, find a 90% Bayesian interval for μ. 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 probability that the population mean is between (Round to four decimal places as needed.) and is 90%.
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 0.7 -2.7 0.7257 0.7580 0.8 0.7881 0.9 0.8159 1.0 0.8413 0.9726 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 0.7291 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 0.9429 0.9382 0.9394 0.9406 0.9441 1.5 0.9463 0.9505 1.6 0.9515 0.9452 0.9474 0.9484 0.9495 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9656 0.9699 0.9664 0.9641 0.9649 0.9693 0.9706 0.9671 1.8 0.9678 1.9 1.9 0.9713 0.9719 0.9732 0.9738 0.9744 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 0.5 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 0.9418 0.9686 0.9750 0.9756 0.9916 2.3 0.9931 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 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 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 0.9997 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 .01 .02 .03 .04 .08 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 0.9996 0.9997 3.3 3.4 .05 .06 .07 .09 The burn time for the first stage of a rocket is a normal random variable with a standard deviation of 0.8 minute. Assume a normal prior distribution for μ with a mean of 10 minutes and a standard deviation of 0.3 minute. If 12 of these rockets are fired and the first stage has an average burn time of 11 minutes, find a 90% Bayesian interval for μ. 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 probability that the population mean is between (Round to four decimal places as needed.) and is 90%.
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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