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According to Chebyshev's theorem, the probability that any random variable assumes a value within 3 8 standard deviations of the mean is at least. If it is known that the probability distribution of a random variable X is normal with mean μ and variance o², what is the exact value of P(μ-30

According to Chebyshev's theorem, the probability that any random variable assumes a value within 3 8 standard deviations of the mean is at least. If it is known that the probability distribution of a random variable X is normal with mean μ and variance o², what is the exact value of P(μ-30

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
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According to Chebyshev's theorem, the probability that any random variable assumes a value within 3 8 standard deviations of the mean is at least. If it is known that the probability distribution of a random variable X is normal with mean μ and variance o², what is the exact value of P(μ-30< X <µ+30)? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. P(μ-30<x<μ+30) = (Round to four decimal places as needed.)
Transcribed Image Text:According to Chebyshev's theorem, the probability that any random variable assumes a value within 3 8 standard deviations of the mean is at least. If it is known that the probability distribution of a random variable X is normal with mean μ and variance o², what is the exact value of P(μ-30< X <µ+30)? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. P(μ-30<x<μ+30) = (Round to four decimal places as needed.)
1 2 B I 5 7 3 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 A Z 8 1 2 3 4 5 6 negative 0.0 B 0 с 0.01 D 0.02 E 0.03 F 0.04 G 0.05 H 0.06 I 0.07 J 0.08 K 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -2.5 0.0062 -2.4 0.0082 0.0084 -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 0.001 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.001 0.001 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.002 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.003 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.004 0.0039 0.0038 0.0037 0.0036 0.006 0.0059 0.0057 0.0055 0.0057 0.0052 0.0051 0.0049 0.0048 0.008 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.3 0.0107 0.0104 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0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.166 0.2119 0.209 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.242 0.2389 0.2358 0.2327 0.2296 0.2296 0.2236 0.2206 0.2177 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 -0.5 0.3085 0.305 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.281 -0.4 0.3446 0.3409 0.3372 0.3336 0.33 0.3264 0.3228 0.3192 0.3156 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.352 0.3483 -0.2 0.4207 0.4168 0.4129 0.409 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5 0.496 0.492 0.488 0.484 0.4801 0.4761 0.4721 0.4681 0.4641 0.117 0.1379 0.1635 0.1611 -0.8 0.1867 -0.7 0.2148 -0.6 0.2743 0.2451 0.2776 0.3121 L M N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 A Z F K с D E 0.01 0.02 0.03 0 0.5 0.504 0.508 0.512 0.1 0.5398 0.5438 0.5478 0.5517 J 0.07 0.08 0.5279 0.5319 H 0.04 0.05 0.06 0.09 0.516 0.5199 0.5239 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0.9979 0.998 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 3 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.999 3.1 0.999 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 0.9986 0.999 0.9993 B 0 G DO L
Transcribed Image Text:1 2 B I 5 7 3 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 A Z 8 1 2 3 4 5 6 negative 0.0 B 0 с 0.01 D 0.02 E 0.03 F 0.04 G 0.05 H 0.06 I 0.07 J 0.08 K 0.09 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -2.5 0.0062 -2.4 0.0082 0.0084 -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 0.001 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.001 0.001 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.002 0.0019 -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.003 0.0029 0.0028 0.0027 0.0026 -2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.004 0.0039 0.0038 0.0037 0.0036 0.006 0.0059 0.0057 0.0055 0.0057 0.0052 0.0051 0.0049 0.0048 0.008 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 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0.1423 0.1401 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.166 0.2119 0.209 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.242 0.2389 0.2358 0.2327 0.2296 0.2296 0.2236 0.2206 0.2177 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 -0.5 0.3085 0.305 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.281 -0.4 0.3446 0.3409 0.3372 0.3336 0.33 0.3264 0.3228 0.3192 0.3156 -0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.352 0.3483 -0.2 0.4207 0.4168 0.4129 0.409 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5 0.496 0.492 0.488 0.484 0.4801 0.4761 0.4721 0.4681 0.4641 0.117 0.1379 0.1635 0.1611 -0.8 0.1867 -0.7 0.2148 -0.6 0.2743 0.2451 0.2776 0.3121 L M N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 A Z F K с D E 0.01 0.02 0.03 0 0.5 0.504 0.508 0.512 0.1 0.5398 0.5438 0.5478 0.5517 J 0.07 0.08 0.5279 0.5319 H 0.04 0.05 0.06 0.09 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0.9305 0.9319 1.5 0.9332 0.9345 0.9357 0.937 0.9382 0.9343 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767 2 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.997 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 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