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(a) Find the mean and the variance o² of X. = 4.6 (Type an integer or a decimal. Do not round.) 20.84 (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. H = 4.6 (Type an integer or a decimal. Do not round.) =0.023 (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 0.9752 (Round to four decimal places as needed.)

(a) Find the mean and the variance o² of X. = 4.6 (Type an integer or a decimal. Do not round.) 20.84 (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. H = 4.6 (Type an integer or a decimal. Do not round.) =0.023 (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 0.9752 (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. x P(X = x) 3 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. = 4.6 (Type an integer or a decimal. Do not round.) ²=0.84 (Type an integer or a decimal. Do not round.) (b) Find the mean μx and the variance o✓ of the mean X for random samples of 36 cherry puffs. H4.6 (Type an integer or a decimal. Do not round.) 0.023 (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 0.9752 (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 shown. x P(X = x) 3 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. = 4.6 (Type an integer or a decimal. Do not round.) ²=0.84 (Type an integer or a decimal. Do not round.) (b) Find the mean μx and the variance o✓ of the mean X for random samples of 36 cherry puffs. H4.6 (Type an integer or a decimal. Do not round.) 0.023 (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 0.9752 (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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