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Two different box-filling machines are used on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is o² = 1 ounce. Experiments are conducted using both machines with sample sizes of 64 each. The sample averages for machines A and B are x = 4.7 ounces and x = 4.9 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) 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) Use the Central Limit Theorem to determine P(X-X≥0.2) under the condition that H₁ = H P(X-X≥0.2) = 0.1292 (b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different? Explain using your answer in (a). Since the probability in (a) negligible, the experiments support the conjecture. is not is

Two different box-filling machines are used on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is o² = 1 ounce. Experiments are conducted using both machines with sample sizes of 64 each. The sample averages for machines A and B are x = 4.7 ounces and x = 4.9 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) 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) Use the Central Limit Theorem to determine P(X-X≥0.2) under the condition that H₁ = H P(X-X≥0.2) = 0.1292 (b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different? Explain using your answer in (a). Since the probability in (a) negligible, the experiments support the conjecture. is not is

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
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Two different box-filling machines are used on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is o² = 1 ounce. Experiments are conducted using both machines with sample sizes of 64 each. The sample averages for machines A and B are x = 4.7 ounces and x = 4.9 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) 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) Use the Central Limit Theorem to determine P(X-XA≥0.2) under the condition that μ₁ = b P(X-X≥0.2) = 0.1292 (b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different? Explain using your answer in (a). Since the probability in (a) negligible, the experiments support the conjecture. is not is
Transcribed Image Text:Two different box-filling machines are used on an assembly line. The critical measurement influenced by these machines is the weight of the product in the boxes. Engineers are quite certain that the variance of the weight of product is o² = 1 ounce. Experiments are conducted using both machines with sample sizes of 64 each. The sample averages for machines A and B are x = 4.7 ounces and x = 4.9 ounces. Engineers are surprised that the two sample averages for the filling machines are so different. Complete parts (a) and (b) 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) Use the Central Limit Theorem to determine P(X-XA≥0.2) under the condition that μ₁ = b P(X-X≥0.2) = 0.1292 (b) Do the aforementioned experiments seem to, in any way, strongly support a conjecture that the population means for the two machines are different? Explain using your answer in (a). Since the probability in (a) negligible, the experiments support the conjecture. is not is
☑= Areas under the Normal Curve z .00 -3.4 0.0003 0.0003 0.0003 .01 .02 .03 .04 -2.9 -2.8 -2.7 -1.0 0.1587 0.1562 0.1539 -0.9 0.1841 -0.8 0.2119 0.2090 -0.7 0.2420 0.2389 -0.6 0.2743 0.2709 -0.5 0.3085 0.3050 -0.0 0.5000 .00 .01 0.4960 0.4920 0.4880 0.4840 0.4801 .02 .03 .04 .05 .06 .07 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 0.0005 0.0005 -3.2 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8 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 0.0080 0.0078 0.0075 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 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 -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 0.1170 -1.1 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1635 0.1611 -0.9 0.1660 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 0.2676 0.2643 0.2611 0.2578 0.2546 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 -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 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1 0.4761 0.4721 0.4681 0.4641 -0.0 .06 .07 .08 .09 .08 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 .09 10 Areas under the Normal Curve 0.0084 -2.3 0.0113 0.0110 -2.2 0.0146 0.0143 -2.1 0.0188 0.0183 -2.0 0.0239 0.0233 -1.9 0.0301 0.0294 1.8 0.0375 0.0367 -1.7 0.0465 0.0455 -1.6 0.0571 0.0559 -1.5 0.0694 0.0681 -1.4 0.0838 0.0823 -1.3 2.3 2.4 2.5 1 2.6 0.2514 0.2483 0.2451 -0.6 2.7 1 0.2810 0.2776 -0.5 2.8 0.3192 0.3156 0.3121 -0.4 2.9 C .05 2 2 .00 .01 .02 .03 .04 .05 .07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2 0.3 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 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 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 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 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 2.1 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 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 0.9934 0.9918 0.9922 0.9920 0.9925 0.9929 0.9927 0.9931 0.9932 0.9936 2.4 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 3.3 0.9995 0.9995 0.9995 0.9996 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 .00 .01 .02 .03 .04 .06 .08 .09 2 .05 2.7 0.9979 0.9979 0.9980 0.9981 2.8 0.9985 0.9985 0.9986 0.9986 2.9 0.9989 0.9989 0.9990 0.9990 3.0 0.9992 0.9992 0.9993 0.9993 3.1 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .06 .07 .08 .09 Q
Transcribed Image Text:☑= Areas under the Normal Curve z .00 -3.4 0.0003 0.0003 0.0003 .01 .02 .03 .04 -2.9 -2.8 -2.7 -1.0 0.1587 0.1562 0.1539 -0.9 0.1841 -0.8 0.2119 0.2090 -0.7 0.2420 0.2389 -0.6 0.2743 0.2709 -0.5 0.3085 0.3050 -0.0 0.5000 .00 .01 0.4960 0.4920 0.4880 0.4840 0.4801 .02 .03 .04 .05 .06 .07 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 0.0005 0.0005 -3.2 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8 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 0.0080 0.0078 0.0075 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 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 -2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 -1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 -1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 -1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 -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 0.1170 -1.1 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1635 0.1611 -0.9 0.1660 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7 0.2676 0.2643 0.2611 0.2578 0.2546 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 -0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 -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 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1 0.4761 0.4721 0.4681 0.4641 -0.0 .06 .07 .08 .09 .08 0.0003 0.0002 -3.4 0.0004 0.0003 -3.3 .09 10 Areas under the Normal Curve 0.0084 -2.3 0.0113 0.0110 -2.2 0.0146 0.0143 -2.1 0.0188 0.0183 -2.0 0.0239 0.0233 -1.9 0.0301 0.0294 1.8 0.0375 0.0367 -1.7 0.0465 0.0455 -1.6 0.0571 0.0559 -1.5 0.0694 0.0681 -1.4 0.0838 0.0823 -1.3 2.3 2.4 2.5 1 2.6 0.2514 0.2483 0.2451 -0.6 2.7 1 0.2810 0.2776 -0.5 2.8 0.3192 0.3156 0.3121 -0.4 2.9 C .05 2 2 .00 .01 .02 .03 .04 .05 .07 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2 0.3 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 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1 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 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8 1.9 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 2.1 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 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 0.9934 0.9918 0.9922 0.9920 0.9925 0.9929 0.9927 0.9931 0.9932 0.9936 2.4 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 3.3 0.9995 0.9995 0.9995 0.9996 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 .00 .01 .02 .03 .04 .06 .08 .09 2 .05 2.7 0.9979 0.9979 0.9980 0.9981 2.8 0.9985 0.9985 0.9986 0.9986 2.9 0.9989 0.9989 0.9990 0.9990 3.0 0.9992 0.9992 0.9993 0.9993 3.1 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 0.9997 0.9997 0.9997 0.9997 0.9998 3.4 .06 .07 .08 .09 Q
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