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2. Given that Z is the standard normal distribution, give the requested values using the z- table or your calculator: a) P(Z< zo) = .8051 Find zo. b) P(Z > zo) = .025 Find zo. c) Find P(.7 sz< 1.3).

2. Given that Z is the standard normal distribution, give the requested values using the z- table or your calculator: a) P(Z< zo) = .8051 Find zo. b) P(Z > zo) = .025 Find zo. c) Find P(.7 sz< 1.3).

A First Course in Probability (10th Edition)
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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Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores 0.09 0.0002 0.0003 0,03 0.5120 0.08 0.5319 0.5714 0.00 0,01 0.02 0,03 0.04 0.05 0.06 0,07 0.08 z 0.00 0.01 0.02 0.04 0,05 0.06 0.07 0.09 0.5000 0.5398 0.5793 -3.4 0.0003 0.0003 0.0003 0,0003 0.0003 0.0003 0.0003 0.0003 0,0003 0.0 0.5040 0.5080 0.5160 0.5199 0.5239 0.5279 0.5359 0.0004 0,0006 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0,0004 0.1 0.5438 0,5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5753 -3.2 0,0007 0.0007 0.0006 0,0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.2 0.5832 0.5871 0,5910 0.5948 0.5987 0,6026 0,6064 0.6103 0,6141 0.0009 0,0012 0.0007 0.0010 0.6217 0.6255 0.6293 0.6664 0.7019 -3.1 0.0010 0.0009 0,0009 0,0008 0.0008 0.0008 0.0008 0.6331 0.6517 0,0007 0.0010 0.3 0.6179 0.6368 0.6406 0.6443 0.6808 0.6480 -3.0 0.0013 0.0013 0.0013 0.0012 0.0011 0.0011 0.0011 0.4 0.6554 0.6591 0.6628 0.6700 0.6736 0.6772 0.6844 0.6879 0.0018 0.0024 0.7123 0.7454 0.7224 0.7549 0.7852 0.8133 -2.9 0,0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0,0014 0.0014 0.5 0,6915 0.6950 0.6985 0.7054 0.7088 0,7157 0.7190 0,0023 0.0032 0.7389 0.7704 0.7995 -2.8 0.0026 0.0025 0,0023 0.0031 0.0041 0.0022 0.0021 0.0021 0.0020 0.0019 0.6 0.7257 0.7291 0,7324 0.7357 0.7673 0.7967 0.7422 0.7486 0.7517 0.0034 0.0045 0.0060 0.0080 0,0026 0.7580 0.7881 0.7794 0.8078 0.8340 -2.7 0.7823 0,0035 0.0047 0.0033 0.0030 0.0040 0.0029 0.0028 0,0038 0.0051 0.0068 0.0089 0.0027 0.0037 0.7611 0.7910 0,7642 0,7939 0.7734 0,8023 0.7764 -2.6 0.0044 0.0043 0.0039 0.0036 0.8 0,8051 0.8106 0.0059 0.0078 0.0102 0.0132 0.0054 0.0071 0,0094 0.0122 0.8212 0.8461 0.8264 0.8508 0.8729 0.8289 0.8531 0.8749 0.8315 0.8554 0.8770 -2.5 0.0062 0.0057 0.0055 0.0052 0.0049 0.0048 0.9 0.8159 0.8186 0,8238 0.8365 0.8389 0.0066 0.0087 0.8438 0.8665 -2.4 0.0082 0.0075 0.0073 0.0069 0.0064 1.0 0.8413 0.8485 0.8577 0.8599 0.8621 0.8643 0.8849 0.9032 0.0099 0.8830 0.9015 0.9177 -2.3 0.0107 0.0104 0.0096 0.0091 0.0084 1.1 0.8686 0,8708 0.8790 0.8810 0.0139 0.0179 0.8997 0.9162 0.9306 0.0125 0.0119 0.0154 0,0116 0.0110 0.8869 0.9049 0.8925 0.,9099 0.9251 0.9382 -2.2 -2.1 0.0136 0.0174 0.0222 0.0129 0.0113 1.2 0.8888 0.8907 0.8944 0.8962 0.8980 0.0170 0.0166 0.0162 0.0158 0.0150 0.0146 0.0143 1.3 0.9066 0.9082 0.9115 0.9131 0.9147 0.9207 0.9345 0.9222 0.9357 -2.0 0.0228 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0,0188 0.0183 1.4 0.9192 0.9236 0.9265 0.9279 0.9292 0.9319 -1.9 0.0287 0.0281 0.0274 0.0268 0,0262 0.0256 0.0250 0.0244 0.0239 0.0233 1.5 0.9332 0.9370 0.9394 0,9406 0.9418 0,9429 0.9441 -1.8 0.0359 0.0351 0.0344 0,0336 0.0329 0.0322 0.0314 0.0307 0.0294 0.0301 0.0375 1.6 0.9452 0.9554 0.9463 0.9474 0.9573 0.9484 0.9495 0.9591 0.9505 0.9515 0.9525 0.9535 0.9545 0.0392 0.0485 0.0401 0.0495 0.0606 0.0735 0.0885 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0384 0.0367 1.7 0.9564 0.9582 0.9599 0.9608 0.9616 0.9625 0.9633 0.0455 0.0559 0.0681 0.0823 0.9649 0.9719 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0475 0.0465 1.8 0.9641 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.0643 0.0778 0.0934 0.9713 0.9772 0.9821 0.9732 0.9788 0.9834 0.9738 0.9793 0.9838 0.9875 0.9750 0.9803 0.9846 0.9761 0.9812 0.9854 -1.5 0.0668 0.0655 0.0630 0.0618 0.0594 0.0582 0.0571 1.9 0.9726 0.9744 0.9756 0.9767 0.0808 0.0968 0.0764 0.0918 0.1093 0.0749 0.0901 0.0694 0.0838 0.9783 0.9830 0.0721 0.0708 0.0853 0.9778 0.9826 0.9798 0.9842 0.9808 0.9850 0.9817 0.9857 0.9890 -1.4 0.0793 0.0951 2.0 -1.3 0.0869 2.1 0.1112 0.1314 0.1075 0.1271 0.1056 0.1251 0.1469 0.1711 0.1020 0.1210 0.9864 0.9896 -1.2 0.1151 0.1131 0.1038 0.1003 0.0985 2.2 0.9861 0.9868 0.9871 0.9878 0.9881 0.9884 0.9887 0.1335 0.1562 0.9906 0.9929 0.1357 0.1230 0.1446 -1.1 0.1292 0.1190 0.1170 2.3 0.9893 0.9898 0.9901 0.9904 0.9909 0.9911 0.9913 0.9916 0.9931 0.9948 0.9961 -1.0 0.1587 0.1539 0,1515 0.1492 0.1423 0.1401 0.1379 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9932 0,9934 0,9936 0.9949 0.9962 0.9951 0.9963 0.9952 0.9964 0.9943 0,9945 0.9959 0.9969 0,9977 0.1660 0.1611 0.1867 0.2148 -0.9 0,1841 0.1814 0.1788 2.5 0.1762 0.2033 0.1736 0.1685 0.1635 0.9938 0.9953 0.9940 0.9941 0.9956 0.9946 0.2061 0.2358 0.2676 0.1977 0.2266 0.2578 2.6 2.7 -0.8 0.2119 0.2090 0.2005 0.1949 0.1922 0.1894 0.9955 0.9957 0.9960 0,2389 0.2709 0.3050 0.3409 0.2177 0.2483 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 -0.7 0.2420 0.2327 0,2296 0.2236 0.2206 0.9965 0.9966 0,9967 0.9970 0.9971 0.9972 0.9973 0.9974 0.9979 0.9985 0.2514 0,2843 0.3192 0.9975 0.9982 0.9987 0.9991 0.9981 0.2546 0.2877 0,9974 0.9981 -0.6 0.2743 0.2643 0.2611 0.2451 2.8 0.9976 0.9978 0.9979 0.9980 0.9986 0.9990 -0.5 0.3085 0.3015 0.2981 0.3336 0.2946 0.2912 0.2810 0.2776 2.9 0.9982 0,9984 0.9984 0.9985 0.9986 0.3446 0.3300 0,3121 0.3483 -0.4 0.3372 0.3264 0.3228 0.3156 3.0 0.9987 0.9987 0.9988 0.9989 0.9989 0.9989 0.9990 0.3707 0.4090 0.3557 0,3936 0.9990 0.9993 0.9995 -0.3 0.3821 0.3783 0.3745 0.3669 0.3632 0.3594 0.3520 3.1 0,9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9993 0.9995 0.9997 -0.2 0.4207 0.4168 0.4129 0.4052 0.4013 0.3974 0.3897 0.3859 3.2 0.9994 0,9994 0.9994 0.9994 0.9995 0.9995 0.9995 0,4404 0.4801 0.4286 0.4681 0.9997 0.9998 0.4602 0.4522 0.4920 0.4364 0.4761 0.4325 0.4721 0.4247 0.4641 -0.1 0.4562 0.4483 0.4443 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 -0.0 0.5000 0.4960 0.4880 0.4840 3.4 0.9997 0,9997 0.9997 0.9997 0.9997 0.9997 0,9997 Note that the probabilities given in this table represent the area to the LEFT of the z-score. The area to the RIGHT of a z-score = 1- the area to the LEFT of the z-score
Transcribed Image Text:Table of Standard Normal Probabilities for Negative Z-scores Table of Standard Normal Probabilities for Positive Z-scores 0.09 0.0002 0.0003 0,03 0.5120 0.08 0.5319 0.5714 0.00 0,01 0.02 0,03 0.04 0.05 0.06 0,07 0.08 z 0.00 0.01 0.02 0.04 0,05 0.06 0.07 0.09 0.5000 0.5398 0.5793 -3.4 0.0003 0.0003 0.0003 0,0003 0.0003 0.0003 0.0003 0.0003 0,0003 0.0 0.5040 0.5080 0.5160 0.5199 0.5239 0.5279 0.5359 0.0004 0,0006 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0,0004 0.1 0.5438 0,5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5753 -3.2 0,0007 0.0007 0.0006 0,0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.2 0.5832 0.5871 0,5910 0.5948 0.5987 0,6026 0,6064 0.6103 0,6141 0.0009 0,0012 0.0007 0.0010 0.6217 0.6255 0.6293 0.6664 0.7019 -3.1 0.0010 0.0009 0,0009 0,0008 0.0008 0.0008 0.0008 0.6331 0.6517 0,0007 0.0010 0.3 0.6179 0.6368 0.6406 0.6443 0.6808 0.6480 -3.0 0.0013 0.0013 0.0013 0.0012 0.0011 0.0011 0.0011 0.4 0.6554 0.6591 0.6628 0.6700 0.6736 0.6772 0.6844 0.6879 0.0018 0.0024 0.7123 0.7454 0.7224 0.7549 0.7852 0.8133 -2.9 0,0019 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0,0014 0.0014 0.5 0,6915 0.6950 0.6985 0.7054 0.7088 0,7157 0.7190 0,0023 0.0032 0.7389 0.7704 0.7995 -2.8 0.0026 0.0025 0,0023 0.0031 0.0041 0.0022 0.0021 0.0021 0.0020 0.0019 0.6 0.7257 0.7291 0,7324 0.7357 0.7673 0.7967 0.7422 0.7486 0.7517 0.0034 0.0045 0.0060 0.0080 0,0026 0.7580 0.7881 0.7794 0.8078 0.8340 -2.7 0.7823 0,0035 0.0047 0.0033 0.0030 0.0040 0.0029 0.0028 0,0038 0.0051 0.0068 0.0089 0.0027 0.0037 0.7611 0.7910 0,7642 0,7939 0.7734 0,8023 0.7764 -2.6 0.0044 0.0043 0.0039 0.0036 0.8 0,8051 0.8106 0.0059 0.0078 0.0102 0.0132 0.0054 0.0071 0,0094 0.0122 0.8212 0.8461 0.8264 0.8508 0.8729 0.8289 0.8531 0.8749 0.8315 0.8554 0.8770 -2.5 0.0062 0.0057 0.0055 0.0052 0.0049 0.0048 0.9 0.8159 0.8186 0,8238 0.8365 0.8389 0.0066 0.0087 0.8438 0.8665 -2.4 0.0082 0.0075 0.0073 0.0069 0.0064 1.0 0.8413 0.8485 0.8577 0.8599 0.8621 0.8643 0.8849 0.9032 0.0099 0.8830 0.9015 0.9177 -2.3 0.0107 0.0104 0.0096 0.0091 0.0084 1.1 0.8686 0,8708 0.8790 0.8810 0.0139 0.0179 0.8997 0.9162 0.9306 0.0125 0.0119 0.0154 0,0116 0.0110 0.8869 0.9049 0.8925 0.,9099 0.9251 0.9382 -2.2 -2.1 0.0136 0.0174 0.0222 0.0129 0.0113 1.2 0.8888 0.8907 0.8944 0.8962 0.8980 0.0170 0.0166 0.0162 0.0158 0.0150 0.0146 0.0143 1.3 0.9066 0.9082 0.9115 0.9131 0.9147 0.9207 0.9345 0.9222 0.9357 -2.0 0.0228 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0,0188 0.0183 1.4 0.9192 0.9236 0.9265 0.9279 0.9292 0.9319 -1.9 0.0287 0.0281 0.0274 0.0268 0,0262 0.0256 0.0250 0.0244 0.0239 0.0233 1.5 0.9332 0.9370 0.9394 0,9406 0.9418 0,9429 0.9441 -1.8 0.0359 0.0351 0.0344 0,0336 0.0329 0.0322 0.0314 0.0307 0.0294 0.0301 0.0375 1.6 0.9452 0.9554 0.9463 0.9474 0.9573 0.9484 0.9495 0.9591 0.9505 0.9515 0.9525 0.9535 0.9545 0.0392 0.0485 0.0401 0.0495 0.0606 0.0735 0.0885 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0384 0.0367 1.7 0.9564 0.9582 0.9599 0.9608 0.9616 0.9625 0.9633 0.0455 0.0559 0.0681 0.0823 0.9649 0.9719 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0475 0.0465 1.8 0.9641 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.0643 0.0778 0.0934 0.9713 0.9772 0.9821 0.9732 0.9788 0.9834 0.9738 0.9793 0.9838 0.9875 0.9750 0.9803 0.9846 0.9761 0.9812 0.9854 -1.5 0.0668 0.0655 0.0630 0.0618 0.0594 0.0582 0.0571 1.9 0.9726 0.9744 0.9756 0.9767 0.0808 0.0968 0.0764 0.0918 0.1093 0.0749 0.0901 0.0694 0.0838 0.9783 0.9830 0.0721 0.0708 0.0853 0.9778 0.9826 0.9798 0.9842 0.9808 0.9850 0.9817 0.9857 0.9890 -1.4 0.0793 0.0951 2.0 -1.3 0.0869 2.1 0.1112 0.1314 0.1075 0.1271 0.1056 0.1251 0.1469 0.1711 0.1020 0.1210 0.9864 0.9896 -1.2 0.1151 0.1131 0.1038 0.1003 0.0985 2.2 0.9861 0.9868 0.9871 0.9878 0.9881 0.9884 0.9887 0.1335 0.1562 0.9906 0.9929 0.1357 0.1230 0.1446 -1.1 0.1292 0.1190 0.1170 2.3 0.9893 0.9898 0.9901 0.9904 0.9909 0.9911 0.9913 0.9916 0.9931 0.9948 0.9961 -1.0 0.1587 0.1539 0,1515 0.1492 0.1423 0.1401 0.1379 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9932 0,9934 0,9936 0.9949 0.9962 0.9951 0.9963 0.9952 0.9964 0.9943 0,9945 0.9959 0.9969 0,9977 0.1660 0.1611 0.1867 0.2148 -0.9 0,1841 0.1814 0.1788 2.5 0.1762 0.2033 0.1736 0.1685 0.1635 0.9938 0.9953 0.9940 0.9941 0.9956 0.9946 0.2061 0.2358 0.2676 0.1977 0.2266 0.2578 2.6 2.7 -0.8 0.2119 0.2090 0.2005 0.1949 0.1922 0.1894 0.9955 0.9957 0.9960 0,2389 0.2709 0.3050 0.3409 0.2177 0.2483 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 -0.7 0.2420 0.2327 0,2296 0.2236 0.2206 0.9965 0.9966 0,9967 0.9970 0.9971 0.9972 0.9973 0.9974 0.9979 0.9985 0.2514 0,2843 0.3192 0.9975 0.9982 0.9987 0.9991 0.9981 0.2546 0.2877 0,9974 0.9981 -0.6 0.2743 0.2643 0.2611 0.2451 2.8 0.9976 0.9978 0.9979 0.9980 0.9986 0.9990 -0.5 0.3085 0.3015 0.2981 0.3336 0.2946 0.2912 0.2810 0.2776 2.9 0.9982 0,9984 0.9984 0.9985 0.9986 0.3446 0.3300 0,3121 0.3483 -0.4 0.3372 0.3264 0.3228 0.3156 3.0 0.9987 0.9987 0.9988 0.9989 0.9989 0.9989 0.9990 0.3707 0.4090 0.3557 0,3936 0.9990 0.9993 0.9995 -0.3 0.3821 0.3783 0.3745 0.3669 0.3632 0.3594 0.3520 3.1 0,9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9993 0.9995 0.9997 -0.2 0.4207 0.4168 0.4129 0.4052 0.4013 0.3974 0.3897 0.3859 3.2 0.9994 0,9994 0.9994 0.9994 0.9995 0.9995 0.9995 0,4404 0.4801 0.4286 0.4681 0.9997 0.9998 0.4602 0.4522 0.4920 0.4364 0.4761 0.4325 0.4721 0.4247 0.4641 -0.1 0.4562 0.4483 0.4443 3.3 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 -0.0 0.5000 0.4960 0.4880 0.4840 3.4 0.9997 0,9997 0.9997 0.9997 0.9997 0.9997 0,9997 Note that the probabilities given in this table represent the area to the LEFT of the z-score. The area to the RIGHT of a z-score = 1- the area to the LEFT of the z-score
2. Given that Z is the standard normal distribution, give the requested values using the z- table or your calculator: a) P(Z< zo) = .8051 Find zo. b) P(Z > zo) = .025 Find zo. c) Find P(.7 <z< 1.3).
Transcribed Image Text:2. Given that Z is the standard normal distribution, give the requested values using the z- table or your calculator: a) P(Z< zo) = .8051 Find zo. b) P(Z > zo) = .025 Find zo. c) Find P(.7 <z< 1.3).
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