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The random variable X, representing the number of cherries in a cherry puff, has the probability distribution show() P(X=x) | 3 0.1 4 5 6 0.4 0.3 0.2 Complete parts (a) through (c) below. 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) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance σ of the mean X for random samples of 36 cherry puffs. (Type an integer or a decimal. Do not round.) 0 = ☐ (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is (Round to four decimal places as needed.)

The random variable X, representing the number of cherries in a cherry puff, has the probability distribution show() P(X=x) | 3 0.1 4 5 6 0.4 0.3 0.2 Complete parts (a) through (c) below. 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) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance σ of the mean X for random samples of 36 cherry puffs. (Type an integer or a decimal. Do not round.) 0 = ☐ (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is (Round to four decimal places as needed.)

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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I need help with this please especially part b

The random variable X, representing the number of cherries in a cherry puff, has the probability distribution show P(X=x) 3 0.1 4 0.4 5 6 0.3 0.2 Complete parts (a) through (c) below. 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) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) 0² (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance o² of the mean X for random samples of 36 cherry puffs. (Type an integer or a decimal. Do not round.) = (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is (Round to four decimal places as needed.)
Transcribed Image Text:The random variable X, representing the number of cherries in a cherry puff, has the probability distribution show P(X=x) 3 0.1 4 0.4 5 6 0.3 0.2 Complete parts (a) through (c) below. 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) Find the mean μ and the variance o² of X. (Type an integer or a decimal. Do not round.) 0² (Type an integer or a decimal. Do not round.) (b) Find the mean μ and the variance o² of the mean X for random samples of 36 cherry puffs. (Type an integer or a decimal. Do not round.) = (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 4.9. The probability is (Round to four decimal places as needed.)
الها Areas under the Normal Curve > > 2 .00 Areas under the Normal Curve .01 .02 .03 .04 0.0129 0.4443 .01 .02 .04 z .00 .01 .02 .03 .04 .05 .06 .07 -3.4 0.0003 0.0003 0.0003 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 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0010 0.0009 -3.1 0.0009 0.0009 0.0008 0.0008 0.0008 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 -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 0.0078 0.0075 0.0080 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 0.0125 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 0.0281 0.0287 0.0268 0.0274 0.0262 0.0256 0.0250 0.0239 0.0244 0.0233 -1.9 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 -1.7 0.0436 0.0427 0.0418 0.0446 0.0409 0.0401 0.0384 0.0375 0.0367 0.0392 -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 0.0918 0.0901 0.0885 0.0934 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 -1.1 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 0.1841 0.1788 0.1762 0.1814 0.1736 0.1711 0.1685 0.1660 -0.9 0.1611 -0.9 0.1635 -0.8 0.2119 0.2061 0.2033 0.2005 0.2090 0.1977 0.1949 0.1922 0.1894 -0.8 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 -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 0.3483 -0.3 -0.2 0.4207 0.4090 0.4013 0.3974 0.4168 0.3897 0.4129 0.3859 -0.2 0.4052 0.3936 0.4602 0.4483 -0.1 0.4562 0.4364 0.4522 0.4325 0.4286 0.4404 -0.1 0.4247 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 .00 .03 .05 .06 .07 .08 .08 .09 2 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 0.0008 0.0007 0.0007 -3.1 0.0011 0.0010 0.0010 -3.0 0.0015 0.0014 0.3 0.0021 0.0020 0.0014 -2.9 0.0019 -2.8 1.6 1.7 1.8 1.9 2.1 1 + 2.9 0.9981 3.0 3.1 .07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 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 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 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8643 1.1 0.8665 0.8686 0.8708 0.8749 0.8729 0.8770 0.8790 0.8810 1.1 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 0.9463 0.9452 0.9474 0.9484 0.9495 0.9505 0.9515 1.6 0.9525 0.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 0.9649 0.9656 0.9641 0.9664 0.9671 0.9693 0.9678 0.9686 0.9706 0.9699 1.8 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 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 0.9963 0.9964 0.9962 2.6 0.9965 2.7 0.9966 0.9967 0.9968 0.9970 0.9969 0.9971 0.9972 0.9973 0.9974 2.7 回 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9990 0.9991 .05 .06 .08 .09 0.5359 0.0 0.5753 0.1 0.6141 0.2 0.9985 0.9986 0.9986 2.9 A 3.2 3.3 A 3.4 0.9991 0.9991 0.9992 0.9992 0.9992 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 0.9989 0.9990 0.9990 3.0 0.9992 0.9993 0.9993 3.1 2 0.9995 0.9995 0.9997 0.9997 .00 .01 0.9995 0.9996 0.9997 0.9997 .02 .03 0.9996 0.9996 0.9997 0.9997 0.9996 0.9997 .04 .05 .06 0.9996 0.9996 0.9997 0.9997 .07 .08 0.9997 0.9998 .09 3.3 3.4 .09 2
Transcribed Image Text:الها Areas under the Normal Curve > > 2 .00 Areas under the Normal Curve .01 .02 .03 .04 0.0129 0.4443 .01 .02 .04 z .00 .01 .02 .03 .04 .05 .06 .07 -3.4 0.0003 0.0003 0.0003 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 -3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0010 0.0009 -3.1 0.0009 0.0009 0.0008 0.0008 0.0008 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 -2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 -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 0.0078 0.0075 0.0080 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 0.0125 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 0.0281 0.0287 0.0268 0.0274 0.0262 0.0256 0.0250 0.0239 0.0244 0.0233 -1.9 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8 -1.7 0.0436 0.0427 0.0418 0.0446 0.0409 0.0401 0.0384 0.0375 0.0367 0.0392 -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 0.0918 0.0901 0.0885 0.0934 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 -1.1 0.1170 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 0.1841 0.1788 0.1762 0.1814 0.1736 0.1711 0.1685 0.1660 -0.9 0.1611 -0.9 0.1635 -0.8 0.2119 0.2061 0.2033 0.2005 0.2090 0.1977 0.1949 0.1922 0.1894 -0.8 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5 -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 0.3483 -0.3 -0.2 0.4207 0.4090 0.4013 0.3974 0.4168 0.3897 0.4129 0.3859 -0.2 0.4052 0.3936 0.4602 0.4483 -0.1 0.4562 0.4364 0.4522 0.4325 0.4286 0.4404 -0.1 0.4247 -0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 .00 .03 .05 .06 .07 .08 .08 .09 2 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 0.0005 0.0005 -3.2 0.0008 0.0007 0.0007 -3.1 0.0011 0.0010 0.0010 -3.0 0.0015 0.0014 0.3 0.0021 0.0020 0.0014 -2.9 0.0019 -2.8 1.6 1.7 1.8 1.9 2.1 1 + 2.9 0.9981 3.0 3.1 .07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 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 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 0.8531 0.8554 0.8577 0.8599 0.8621 1.0 0.8643 1.1 0.8665 0.8686 0.8708 0.8749 0.8729 0.8770 0.8790 0.8810 1.1 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5 0.9463 0.9452 0.9474 0.9484 0.9495 0.9505 0.9515 1.6 0.9525 0.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 0.9649 0.9656 0.9641 0.9664 0.9671 0.9693 0.9678 0.9686 0.9706 0.9699 1.8 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 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 0.9963 0.9964 0.9962 2.6 0.9965 2.7 0.9966 0.9967 0.9968 0.9970 0.9969 0.9971 0.9972 0.9973 0.9974 2.7 回 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9990 0.9991 .05 .06 .08 .09 0.5359 0.0 0.5753 0.1 0.6141 0.2 0.9985 0.9986 0.9986 2.9 A 3.2 3.3 A 3.4 0.9991 0.9991 0.9992 0.9992 0.9992 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 0.9989 0.9990 0.9990 3.0 0.9992 0.9993 0.9993 3.1 2 0.9995 0.9995 0.9997 0.9997 .00 .01 0.9995 0.9996 0.9997 0.9997 .02 .03 0.9996 0.9996 0.9997 0.9997 0.9996 0.9997 .04 .05 .06 0.9996 0.9996 0.9997 0.9997 .07 .08 0.9997 0.9998 .09 3.3 3.4 .09 2
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