A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Areas under the Normal Curve Areas under the Normal Curve = .00 .01 .02 -3.4 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 -3.2 0.0007 0.0007 0.0006 -3.1 0.0010 0.0009 0.0009 -3.0 0.0013 0.0013 0.0013 .03 0.0003 0.0004 .04 0.0003 0.0003 .05 0.0006 0.0009 0.0012 -1.8 0.0359 0.0351 田 ୧. -0.0 ¡A .00 .01 0.4404 0.4920 0.4880 0.4840 0.4801 .02 .03 .04 .05 0.0006 0.0005 0.0008 0.0008 0.0011 0.0011 -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 0.0021 0.0020 0.0019 -2.8 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.7 -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 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 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 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1 -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 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0,0985 -1.2 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4364 0.4325 0.4286 0.5000 0.4960 0.0004 0.0004 0.0006 0.0006 0.0008 0.0008 0.0012 0.0011 .06 .07 0.0003 0.0003 0.0004 0.0004 .08 .09 0.0003 0.0002 Z .01 .02 .03 -3.4 0.0 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 0.0007 0.0007 -3.1 0.0010 0.0010 -3.0 0.1 0.2 0.3 0.4 0.5 .00 0.5000 0.5040 0.5080 0.5120 0.5398 0.5438 0.5478 0.5517 0.5793 0.5832 0.5871 0.5910 0.6179 0.6217 0.6255 0.6293 0.6554 0.6591 0.6628 0.6664 0.6915 0.6950 0.6985 0.7019 0.7157 0.7190 0.7224 0.5 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6 .04 .05 .06 0.5160 0.5199 0.5239 0.5557 0.5596 0.5636 0.5948 0.5987 0.6026 0.6331 0.6368 0.6406 0.6700 0.6736 0.6772 0.7054 0.7088 0.7123 .07 .08 .09 2 0.5279 0.5319 0.5359 0.0 0.5675 0.5714 0.5753 0.1 0.6064 0.6103 0.6141 0.2 0.6443 0.6480 0.6517 0.3 0.6808 0.6844 0.6879 0.4 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 1.0 0.8413 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 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9515 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 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0,9906 0,9909 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 0.8810 0.8830 1.1 0.8980 0.8997 0.9015 1.2 0.9147 0.9162 0.9177 1.3 0.9292 0.9306 0.9319 1.4 0.9505 0.9756 0.9761 0.9767 1.9 0.9808 0.9812 0,9817 2.0 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9890 2.2 0.9911 0.9913 0.9916 2.3 0.2148 -0.7 0.9932 0.9934 0.9936 2.4 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 2.6 0,9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 1 0.2483 0.2451 -0.6 0.2810 0.2776 -0.5 田 0.4761 0.4721 0.4681 .06 .07 .08 0.3483 -0.3 0.3859 -0.2 0.4247 -0.1 0.4641 -0.0 .09 2 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 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 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .00 .01 .02 .03 .04 .06 .07 .08 .09 0.9997 .05 Z
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Transcribed Image Text:Areas under the Normal Curve Areas under the Normal Curve = .00 .01 .02 -3.4 0.0003 0.0003 0.0003 -3.3 0.0005 0.0005 0.0005 -3.2 0.0007 0.0007 0.0006 -3.1 0.0010 0.0009 0.0009 -3.0 0.0013 0.0013 0.0013 .03 0.0003 0.0004 .04 0.0003 0.0003 .05 0.0006 0.0009 0.0012 -1.8 0.0359 0.0351 田 ୧. -0.0 ¡A .00 .01 0.4404 0.4920 0.4880 0.4840 0.4801 .02 .03 .04 .05 0.0006 0.0005 0.0008 0.0008 0.0011 0.0011 -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 0.0021 0.0020 0.0019 -2.8 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 -2.7 -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 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 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 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1 -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 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.9 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -1.7 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 -1.3 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0,0985 -1.2 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 -1.1 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 -0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4364 0.4325 0.4286 0.5000 0.4960 0.0004 0.0004 0.0006 0.0006 0.0008 0.0008 0.0012 0.0011 .06 .07 0.0003 0.0003 0.0004 0.0004 .08 .09 0.0003 0.0002 Z .01 .02 .03 -3.4 0.0 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 0.0007 0.0007 -3.1 0.0010 0.0010 -3.0 0.1 0.2 0.3 0.4 0.5 .00 0.5000 0.5040 0.5080 0.5120 0.5398 0.5438 0.5478 0.5517 0.5793 0.5832 0.5871 0.5910 0.6179 0.6217 0.6255 0.6293 0.6554 0.6591 0.6628 0.6664 0.6915 0.6950 0.6985 0.7019 0.7157 0.7190 0.7224 0.5 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6 .04 .05 .06 0.5160 0.5199 0.5239 0.5557 0.5596 0.5636 0.5948 0.5987 0.6026 0.6331 0.6368 0.6406 0.6700 0.6736 0.6772 0.7054 0.7088 0.7123 .07 .08 .09 2 0.5279 0.5319 0.5359 0.0 0.5675 0.5714 0.5753 0.1 0.6064 0.6103 0.6141 0.2 0.6443 0.6480 0.6517 0.3 0.6808 0.6844 0.6879 0.4 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 1.0 0.8413 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 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9515 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 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0,9906 0,9909 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8790 0.8810 0.8830 1.1 0.8980 0.8997 0.9015 1.2 0.9147 0.9162 0.9177 1.3 0.9292 0.9306 0.9319 1.4 0.9505 0.9756 0.9761 0.9767 1.9 0.9808 0.9812 0,9817 2.0 0.9850 0.9854 0.9857 2.1 0.9884 0.9887 0.9890 2.2 0.9911 0.9913 0.9916 2.3 0.2148 -0.7 0.9932 0.9934 0.9936 2.4 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 2.6 0,9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 1 0.2483 0.2451 -0.6 0.2810 0.2776 -0.5 田 0.4761 0.4721 0.4681 .06 .07 .08 0.3483 -0.3 0.3859 -0.2 0.4247 -0.1 0.4641 -0.0 .09 2 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9 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 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .00 .01 .02 .03 .04 .06 .07 .08 .09 0.9997 .05 Z
A coin is tossed 576 times. Use the normal curve approximation to find the probability of obtaining (a) between 269 and 301 heads inclusive; (b) exactly 292 heads; (c) fewer than 261 or more than 321 heads. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The probability is (Round to four decimal places as needed.) (b) The probability is ☐ (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.)
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Transcribed Image Text:A coin is tossed 576 times. Use the normal curve approximation to find the probability of obtaining (a) between 269 and 301 heads inclusive; (b) exactly 292 heads; (c) fewer than 261 or more than 321 heads. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The probability is (Round to four decimal places as needed.) (b) The probability is ☐ (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.)
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Step 1: Determine the given variables.
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Step 2: Use the normal curve approximation.
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Step 3: Find the probability of obtaining heads between 269 and 301 ( inclusive ).
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Step 4: Find the probability of obtaining exactly 292 heads.
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Step 5: Find the probability of obtaining fewer than 261 or more than 321 heads.
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