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 PXB-XA≥0.2)=

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Areas under the Normal Curve
Areas under the Normal Curve
名
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
社
0.0003
-0.0
2
-3.4 0.0003 0.0003 0.0003
0.0003 0.0003
0.0003 0.0002
0.0003
-3.4
0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.3
-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 0.0017
0.0016
-2.9
0.0018
0.0016
0.0015 0.0015 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8
-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
0.0080
0.0075 0.0073
0.0069 0.0068
-2.4 0.0082
0.0066
0.0078
0.0071
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 0.0129 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
0.0287
0.0274 0.0268
-1.9
0.0262 0.0256
0.0281
0.0250 0.0244 0.0239 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
0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -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
0.0793 0.0778
-1.4
0.0764 0.0749
0.0808
0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901
0.0885 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 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492
0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-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 0.4168 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
0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721
0.4681 0.4641 -0.0
.00
.01
.02
.03
.04
.06
.07
.08
.09
.05
0
0.0
0.3
0.4
0.0014
-2.9
2.8
田
.00
.01
.02
.03
.04
0.5000 0.5040 0.5080 0.5120 0.5160
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
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.6554
0.6700
0.6591 0.6628 0.6664
0.6808
0.6736 0.6772
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
0.8264
0.8159
0.8238
0.8289
0.8186
0.8315
0.8212
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
0.9236 0.9251 0.9265
0.9306 0.9319
0.9207 0.9222
0.9279 0.9292
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
0.9515 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
0.9726
0.9738 0.9744
0.9756 0.9761
0.9719
1.9
0.9732
0.9750
0.9767
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
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 0.9962 0.9963 0.9964 2.6
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986
2.9
0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
.05
.07
.06
.08
.09
0.5199 0.5239 0.5279 0.5319 0.5359 0.0
0.9505
3.4
0.9997
2
A
2
.00
0.9997
.01
0.9997
.02
0.9997
.03
0.9997
.04
0.9997
.05
0.9997
.06
0.9997
.07
0.9997
0.9998
3.4
.08
.09
Z
Transcribed Image Text:Areas under the Normal Curve Areas under the Normal Curve 名 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 社 0.0003 -0.0 2 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.0003 -3.4 0.0003 -3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.3 -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 0.0017 0.0016 -2.9 0.0018 0.0016 0.0015 0.0015 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8 -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 0.0080 0.0075 0.0073 0.0069 0.0068 -2.4 0.0082 0.0066 0.0078 0.0071 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 0.0129 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 0.0287 0.0274 0.0268 -1.9 0.0262 0.0256 0.0281 0.0250 0.0244 0.0239 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 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -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 0.0793 0.0778 -1.4 0.0764 0.0749 0.0808 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 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 0.1170 -1.1 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8 -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 0.4168 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 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0 .00 .01 .02 .03 .04 .06 .07 .08 .09 .05 0 0.0 0.3 0.4 0.0014 -2.9 2.8 田 .00 .01 .02 .03 .04 0.5000 0.5040 0.5080 0.5120 0.5160 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 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3 0.6554 0.6700 0.6591 0.6628 0.6664 0.6808 0.6736 0.6772 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 0.8264 0.8159 0.8238 0.8289 0.8186 0.8315 0.8212 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 0.9236 0.9251 0.9265 0.9306 0.9319 0.9207 0.9222 0.9279 0.9292 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 0.9515 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 0.9726 0.9738 0.9744 0.9756 0.9761 0.9719 1.9 0.9732 0.9750 0.9767 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 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 0.9962 0.9963 0.9964 2.6 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 2.9 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.1 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3 .05 .07 .06 .08 .09 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 0.9505 3.4 0.9997 2 A 2 .00 0.9997 .01 0.9997 .02 0.9997 .03 0.9997 .04 0.9997 .05 0.9997 .06 0.9997 .07 0.9997 0.9998 3.4 .08 .09 Z
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 μA - HB-
P(XB-XA≥0.2)=
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-X≥0.2) under the condition that μA - HB- P(XB-XA≥0.2)=
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