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Answer the following questions using the z-score chart( attached below) or by using a spreadsheet.  1. For a mean of 153 and standard deviation of 25, find .    2. IQ scores of people around the World are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius?   3. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg? b. A car is said to be in the 90th percentile.  How much does it weigh?

Answer the following questions using the z-score chart( attached below) or by using a spreadsheet.  1. For a mean of 153 and standard deviation of 25, find .    2. IQ scores of people around the World are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius?   3. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg. a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg? b. A car is said to be in the 90th percentile.  How much does it weigh?

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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Answer the following questions using the z-score chart( attached below) or by using a spreadsheet. 

1. For a mean of 153 and standard deviation of 25, find . 
 

2. IQ scores of people around the World are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 140. What percent of the population is considered genius?
 

3. The Weights of 100 remote control cars at a competition are approximately normally distributed. The average weight is 3.2 kg, with a standard deviation of 0.4 kg.

a. How many remote control cars would be disqualified if it were against the rules to have a car with a weight of more than 4 kg or less than 2.4 kg?

b. A car is said to be in the 90th percentile.  How much does it weigh?

Standard Normal Cumulative Probability Table Cumulative probabilities for NEGATIVE z-values are shown in the following table: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 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 0.0023 0.0016 0.0015 0.0021 0.0029 0.0039 0.0052 0.0015 0.0014 0.0014 0.0026 0.0035 0.0047 -2.8 0.0025 0.0024 0.0023 0.0022 0.0021 0.0020 0.0019 0.0030 0.0040 0.0028 0.0027 -2.7 -2.6 -2.5 0.0034 0.0045 0.0033 0.0032 0.0031 0.0026 0.0036 0.0044 0.0059 0.0043 0.0057 0.0041 0.0038 0.0037 0.0062 0.0060 0.0055 0.0054 0.0051 0.0049 0.0048 -2.4 -2.3 0.0082 0.0080 0.0078 0.0075 0.0073 0.0096 0.0125 0.0071 0.0069 0.0068 0.0066 0.0087 0.0113 0.0064 0.0104 0.0136 0.0102 0.0132 0.0089 0.0116 0.0107 0.0099 0.0091 0.0094 0.0122 0.0158 0.0084 0.0110 0.0143 0.0183 -2.2 0.0139 0.0129 0.0119 -2.1 0.0179 0.0174 0.0170 0.0217 0.0166 0.0212 0.0162 0.0207 0.0154 0.0197 0.0150 0.0192 0.0146 0.0188 -2.0 0.0228 0.0222 0.0202 0.0268 0.0336 0.0418 -1.9 0.0262 0.0256 0.0287 0.0359 0.0446 0.0548 0.0281 0.0351 0.0436 0.0537 0.0274 0.0344 0.0427 0.0526 0.0643 0.0250 0.0314 0.0392 0.0485 0.0594 0.0244 0.0307 0.0384 0.0475 0.0239 0.0301 0.0375 0.0465 0.0571 0.0233 0.0294 0.0367 0.0455 0.0559 -1.8 0.0329 0.0409 0.0505 0.0618 0.0322 0.0401 0.0495 0.0606 -1.7 -1.6 -1.5 0.0516 0.0630 0.0668 0.0655 0.0582 0.0764 0.0918 0.0749 0.0901 0.0694 0.0838 -1.4 0.0735 0.0808 0.0968 0.0793 0.0951 0.0778 0.0934 0.0721 0.0869 0.0708 0.0681 0.0823 -1.3 0.0885 0.0853 -1.2 -1.1 -1.0 0.1093 0.1292 0.1515 0.1056 0.1151 0.1357 0.1587 0.1131 0.1335 0.1562 0.1112 0.1314 0.1539 0.1075 0.1271 0.1492 0.1251 0.1469 0.1038 0.1230 0.1020 0.1210 0.1423 0.1003 0.1190 0.1401 0.0985 0.1170 0.1379 0.1446 -0.9 -0.8 -0.7 -0.6 -0.5 0.1841 0.2119 0.2420 0.2743 0.3085 0.1814 0.2090 0.2389 0.2709 0.3050 0.1788 0.2061 0.2358 0.2676 0.3015 0.1762 0.2033 0.2327 0.2643 0.2981 0.1736 0.2005 0.2296 0.1711 0.1977 0.2266 0.2578 0.2912 0.1685 0.1949 0.2236 0.2546 0.2877 0.1660 0.1922 0.2206 0.2514 0.2843 0.1635 0.1894 0.2177 0.1611 0.1867 0.2148 0.2451 0.2776 0.2611 0.2946 0.2483 0.2810 0.3336 0.3156 -0.4 -0.3 -0.2 -0.1 0.0 0.3446 0.3821 0.4207 0.4602 0.5000 0.3409 0.3783 0.4168 0.4562 0.4960 0.3372 0.3745 0.4129 0.4522 0.4920 0.3707 0.4090 0.4483 0.4880 0.3300 0.3669 0.4052 0.4443 0.4840 0.3264 0.3632 0.4013 0.4404 0.4801 0.3228 0.3594 0.3974 0.4364 0.4761 0.3192 0.3557 0.3936 0.4325 0.4721 0.3520 0.3897 0.4286 0.4681 0.3121 0.3483 0.3859 0.4247 0.4641
Transcribed Image Text:Standard Normal Cumulative Probability Table Cumulative probabilities for NEGATIVE z-values are shown in the following table: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.2 0.0007 0.0007 0.0006 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 0.0023 0.0016 0.0015 0.0021 0.0029 0.0039 0.0052 0.0015 0.0014 0.0014 0.0026 0.0035 0.0047 -2.8 0.0025 0.0024 0.0023 0.0022 0.0021 0.0020 0.0019 0.0030 0.0040 0.0028 0.0027 -2.7 -2.6 -2.5 0.0034 0.0045 0.0033 0.0032 0.0031 0.0026 0.0036 0.0044 0.0059 0.0043 0.0057 0.0041 0.0038 0.0037 0.0062 0.0060 0.0055 0.0054 0.0051 0.0049 0.0048 -2.4 -2.3 0.0082 0.0080 0.0078 0.0075 0.0073 0.0096 0.0125 0.0071 0.0069 0.0068 0.0066 0.0087 0.0113 0.0064 0.0104 0.0136 0.0102 0.0132 0.0089 0.0116 0.0107 0.0099 0.0091 0.0094 0.0122 0.0158 0.0084 0.0110 0.0143 0.0183 -2.2 0.0139 0.0129 0.0119 -2.1 0.0179 0.0174 0.0170 0.0217 0.0166 0.0212 0.0162 0.0207 0.0154 0.0197 0.0150 0.0192 0.0146 0.0188 -2.0 0.0228 0.0222 0.0202 0.0268 0.0336 0.0418 -1.9 0.0262 0.0256 0.0287 0.0359 0.0446 0.0548 0.0281 0.0351 0.0436 0.0537 0.0274 0.0344 0.0427 0.0526 0.0643 0.0250 0.0314 0.0392 0.0485 0.0594 0.0244 0.0307 0.0384 0.0475 0.0239 0.0301 0.0375 0.0465 0.0571 0.0233 0.0294 0.0367 0.0455 0.0559 -1.8 0.0329 0.0409 0.0505 0.0618 0.0322 0.0401 0.0495 0.0606 -1.7 -1.6 -1.5 0.0516 0.0630 0.0668 0.0655 0.0582 0.0764 0.0918 0.0749 0.0901 0.0694 0.0838 -1.4 0.0735 0.0808 0.0968 0.0793 0.0951 0.0778 0.0934 0.0721 0.0869 0.0708 0.0681 0.0823 -1.3 0.0885 0.0853 -1.2 -1.1 -1.0 0.1093 0.1292 0.1515 0.1056 0.1151 0.1357 0.1587 0.1131 0.1335 0.1562 0.1112 0.1314 0.1539 0.1075 0.1271 0.1492 0.1251 0.1469 0.1038 0.1230 0.1020 0.1210 0.1423 0.1003 0.1190 0.1401 0.0985 0.1170 0.1379 0.1446 -0.9 -0.8 -0.7 -0.6 -0.5 0.1841 0.2119 0.2420 0.2743 0.3085 0.1814 0.2090 0.2389 0.2709 0.3050 0.1788 0.2061 0.2358 0.2676 0.3015 0.1762 0.2033 0.2327 0.2643 0.2981 0.1736 0.2005 0.2296 0.1711 0.1977 0.2266 0.2578 0.2912 0.1685 0.1949 0.2236 0.2546 0.2877 0.1660 0.1922 0.2206 0.2514 0.2843 0.1635 0.1894 0.2177 0.1611 0.1867 0.2148 0.2451 0.2776 0.2611 0.2946 0.2483 0.2810 0.3336 0.3156 -0.4 -0.3 -0.2 -0.1 0.0 0.3446 0.3821 0.4207 0.4602 0.5000 0.3409 0.3783 0.4168 0.4562 0.4960 0.3372 0.3745 0.4129 0.4522 0.4920 0.3707 0.4090 0.4483 0.4880 0.3300 0.3669 0.4052 0.4443 0.4840 0.3264 0.3632 0.4013 0.4404 0.4801 0.3228 0.3594 0.3974 0.4364 0.4761 0.3192 0.3557 0.3936 0.4325 0.4721 0.3520 0.3897 0.4286 0.4681 0.3121 0.3483 0.3859 0.4247 0.4641
Standard Normal Cumulative Probability Table Cumulative probabilities for POSITIVE z-values are shown in the following table: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6443 0.6808 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6628 0.6293 0.6331 0.6368 0.6406 0.6480 0.6517 0.6879 0.4 0.6554 0.6591 0.6664 0.6700 0.6736 0.6772 0.6844 0.6950 0.7291 0.5 0.6915 0.6985 0.7019 0.7088 0.7157 0.7054 0.7389 0.7123 0.7190 0.7224 0.6 0.7257 0.7324 0.7357 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7939 0.7673 0.7704 0.7734 0.7764 0.8051 0.8315 0.7794 0.7823 0.7852 0.8 0.9 0.7881 0.7910 0.7967 0.7995 0.8023 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8621 0.8461 0.8686 0.8888 0.9066 0.8485 0.8508 0.8531 0.8554 0.8770 0.8962 0.9131 0.9279 0.8577 0.8790 0.8980 0.9147 0.8599 1.1 0.8643 0.8665 0.8708 0.8729 0.8749 0.8810 0.8830 0.9015 0.8907 1.2 1.3 0.8849 0.9032 0.8869 0.8925 0.8944 0.8997 0.9162 0.9049 0.9082 0.9099 0.9115 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9292 0.9306 0.9319 0.9357 0.9474 0.9573 0.9656 0.9726 1.5 1.6 0.9406 0.9515 0.9332 0.9452 0.9554 0.9641 0.9713 0.9345 0.9463 0.9564 0.9649 0.9719 0.9370 0.9484 0.9582 0.9664 0.9732 0.9382 0.9495 0.9591 0.9671 0.9738 0.9394 0.9418 0.9525 0.9616 0.9693 0.9756 0.9429 0.9441 0.9545 0.9633 0.9505 0.9535 0.9625 0.9699 0.9761 1.7 1.8 1.9 0.9599 0.9678 0.9744 0.9608 0.9686 0.9750 0.9706 0.9767 0.9808 0.9812 2.0 2.1 2.2 2.3 2.4 0.9772 0.9821 0.9861 0.9893 0.9918 0.9778 0.9826 0.9864 0.9896 0.9920 0.9783 0.9830 0.9868 0.9898 0.9922 0.9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 0.9798 0.9842 0.9878 0.9906 0.9929 0.9803 0.9846 0.9881 0.9909 0.9931 0.9817 0.9857 0.9890 0.9916 0.9936 0.9850 0.9884 0.9854 0.9887 0.9913 0.9934 0.9911 0.9932 0.9945 2.5 2.6 0.9938 0.9953 0.9940 0.9955 0.9941 0.9956 0.9943 0.9957 0.9946 0.9960 0.9948 0.9961 0.9949 0.9962 0.9951 0.9963 0.9973 0.9980 0.9986 0.9952 0.9964 0.9959 2.7 2.8 2.9 0.9965 0.9974 0.9981 0.9966 0.9975 0.9982 0.9967 0.9976 0.9982 0.9968 0.9977 0.9983 0.9969 0.9977 0.9984 0.9970 0.9978 0.9984 0.9971 0.9979 0.9972 0.9979 0.9985 0.9974 0.9981 0.9986 0.9985 3.0 3.1 3.2 3.3 0.9987 0.9990 0.9993 0.9995 0.9987 0.9991 0.9993 0.9995 0.9987 0.9991 0.9994 0.9995 0.9988 0.9991 0.9994 0.9996 0.9997 0.9988 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9989 0.9992 0.9995 0.9996 0.9990 0.9993 0.9995 0.9996 0.9990 0.9993 0.9995 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
Transcribed Image Text:Standard Normal Cumulative Probability Table Cumulative probabilities for POSITIVE z-values are shown in the following table: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6443 0.6808 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6628 0.6293 0.6331 0.6368 0.6406 0.6480 0.6517 0.6879 0.4 0.6554 0.6591 0.6664 0.6700 0.6736 0.6772 0.6844 0.6950 0.7291 0.5 0.6915 0.6985 0.7019 0.7088 0.7157 0.7054 0.7389 0.7123 0.7190 0.7224 0.6 0.7257 0.7324 0.7357 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7939 0.7673 0.7704 0.7734 0.7764 0.8051 0.8315 0.7794 0.7823 0.7852 0.8 0.9 0.7881 0.7910 0.7967 0.7995 0.8023 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8621 0.8461 0.8686 0.8888 0.9066 0.8485 0.8508 0.8531 0.8554 0.8770 0.8962 0.9131 0.9279 0.8577 0.8790 0.8980 0.9147 0.8599 1.1 0.8643 0.8665 0.8708 0.8729 0.8749 0.8810 0.8830 0.9015 0.8907 1.2 1.3 0.8849 0.9032 0.8869 0.8925 0.8944 0.8997 0.9162 0.9049 0.9082 0.9099 0.9115 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9292 0.9306 0.9319 0.9357 0.9474 0.9573 0.9656 0.9726 1.5 1.6 0.9406 0.9515 0.9332 0.9452 0.9554 0.9641 0.9713 0.9345 0.9463 0.9564 0.9649 0.9719 0.9370 0.9484 0.9582 0.9664 0.9732 0.9382 0.9495 0.9591 0.9671 0.9738 0.9394 0.9418 0.9525 0.9616 0.9693 0.9756 0.9429 0.9441 0.9545 0.9633 0.9505 0.9535 0.9625 0.9699 0.9761 1.7 1.8 1.9 0.9599 0.9678 0.9744 0.9608 0.9686 0.9750 0.9706 0.9767 0.9808 0.9812 2.0 2.1 2.2 2.3 2.4 0.9772 0.9821 0.9861 0.9893 0.9918 0.9778 0.9826 0.9864 0.9896 0.9920 0.9783 0.9830 0.9868 0.9898 0.9922 0.9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 0.9798 0.9842 0.9878 0.9906 0.9929 0.9803 0.9846 0.9881 0.9909 0.9931 0.9817 0.9857 0.9890 0.9916 0.9936 0.9850 0.9884 0.9854 0.9887 0.9913 0.9934 0.9911 0.9932 0.9945 2.5 2.6 0.9938 0.9953 0.9940 0.9955 0.9941 0.9956 0.9943 0.9957 0.9946 0.9960 0.9948 0.9961 0.9949 0.9962 0.9951 0.9963 0.9973 0.9980 0.9986 0.9952 0.9964 0.9959 2.7 2.8 2.9 0.9965 0.9974 0.9981 0.9966 0.9975 0.9982 0.9967 0.9976 0.9982 0.9968 0.9977 0.9983 0.9969 0.9977 0.9984 0.9970 0.9978 0.9984 0.9971 0.9979 0.9972 0.9979 0.9985 0.9974 0.9981 0.9986 0.9985 3.0 3.1 3.2 3.3 0.9987 0.9990 0.9993 0.9995 0.9987 0.9991 0.9993 0.9995 0.9987 0.9991 0.9994 0.9995 0.9988 0.9991 0.9994 0.9996 0.9997 0.9988 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9989 0.9992 0.9995 0.9996 0.9990 0.9993 0.9995 0.9996 0.9990 0.9993 0.9995 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
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