Problem 1 (25 points) Assume your company builds a component that is comprised o

Question

Problem 1 (25 points) Assume your company builds a component that is comprised of three panels. You build each of the panels using a different process and tooling. Panel 1 uses a tool that wears out consistently over time. Therefore the variation in panel height is uniformly distributed between 2.0 and 2.1 mm with the variation largely related to tool wear. Panels 2 and 3 have well defined, stable, and in-control processes. Therefore, the variation in panel height is a function of the natural variation inherent in their respective processes. Panel 2 height is normally distributed with a mean of 4.0 mm and standard deviation of 0.1 mm. Panel 3 height is normally distributed with a mean of 2.0 mmm and standard deviation of 0.05 mm. The customer specification has a maximum height of 8.2 mm. Any components greater than 8.2 mm are rejected. Use Monte Carlo simulation to determine the reject rate for this component. Reject anything> 8.2 mm Panel 3 Normal (2.0, 0.05) Panel 2 Normal (4.0, 0.1) Panel 1 Uniform (2.0, 2.1)

Explanation / Answer

We genrated 500 samples using Monte Carlo simlution for three panels:

Now, we calculated the rejection rate :

Panel 1 Panel 2 Panel 3 Total height Reject 2.0145 3.9724 1.9550 7.9419 No 2.0089 4.0032 1.9212 7.9334 No 2.0285 4.1012 1.9653 8.0951 No 2.0906 3.9452 1.9306 7.9665 No 2.0023 4.0079 1.9898 8.0000 No 2.0421 4.1007 1.9598 8.1026 No 2.0428 4.2195 2.0517 8.3140 Yes 2.0968 3.9521 1.9460 7.9949 No 2.0667 4.0190 1.9882 8.0738 No 2.0105 4.1952 1.9898 8.1955 No 2.0217 4.1868 2.0356 8.2441 Yes 2.0008 4.0630 2.0182 8.0820 No 2.0530 4.0530 2.0153 8.1213 No 2.0950 4.1682 1.9736 8.2368 Yes 2.0222 3.9749 2.0019 7.9991 No 2.0833 4.2323 1.9799 8.2955 Yes 2.0143 3.9517 1.9627 7.9287 No 2.0012 4.1363 2.0065 8.1439 No 2.0842 3.9631 2.0613 8.1086 No 2.0053 4.1526 2.0313 8.1892 No 2.0763 3.8704 2.0359 7.9827 No 2.0760 4.0067 1.9254 8.0081 No 2.0427 3.8920 1.9646 7.8994 No 2.0835 3.9093 1.9560 7.9488 No 2.0729 3.8976 1.9735 7.9441 No 2.0155 3.9225 2.0053 7.9432 No 2.0677 4.0767 1.9677 8.1121 No 2.0839 3.9323 2.0388 8.0551 No 2.0286 4.0320 2.0170 8.0775 No 2.0287 4.1423 1.8916 8.0627 No 2.0344 4.1157 2.1153 8.2655 Yes 2.0230 4.0285 1.9877 8.0392 No 2.0172 4.0576 2.0064 8.0812 No 2.0741 4.0394 1.9657 8.0791 No 2.0776 3.7880 1.9770 7.8426 No 2.0176 3.8889 1.9827 7.8892 No 2.0751 4.0014 2.0204 8.0969 No 2.0327 4.0493 1.9767 8.0586 No 2.0328 3.9604 2.0433 8.0366 No 2.0738 4.1498 1.9397 8.1633 No 2.0962 3.9896 2.0492 8.1351 No 2.0359 4.0347 1.9873 8.0579 No 2.0173 4.0009 1.8932 7.9115 No 2.0561 3.9223 1.9654 7.9437 No 2.0874 3.8534 2.0540 7.9948 No 2.0112 3.8995 1.9005 7.8112 No 2.0545 4.0143 1.9708 8.0397 No 2.0271 3.8780 1.9921 7.8973 No 2.0126 4.0029 1.9532 7.9687 No 2.0626 4.0397 2.0539 8.1562 No 2.0947 3.8669 1.9137 7.8752 No 2.0979 4.2696 2.0006 8.3681 Yes 2.0031 4.0510 1.9888 8.0429 No 2.0519 4.0435 1.9772 8.0726 No 2.0348 3.8817 2.0180 7.9345 No 2.0806 3.9825 1.9545 8.0176 No 2.0632 4.0485 2.0163 8.1280 No 2.0952 3.9475 2.0893 8.1320 No 2.0913 4.1637 2.0386 8.2936 Yes 2.0831 3.8907 2.0464 8.0202 No 2.0479 4.0990 2.0484 8.1953 No 2.0406 3.9787 1.8810 7.9003 No 2.0282 4.0525 1.9984 8.0791 No 2.0367 3.8828 2.0230 7.9425 No 2.0426 4.0198 2.0449 8.1073 No 2.0439 4.1454 1.8963 8.0856 No 2.0941 4.0202 2.0462 8.1606 No 2.0980 3.9826 2.0548 8.1354 No 2.0206 3.9266 2.0438 7.9910 No 2.0062 4.1425 2.1871 8.3357 Yes 2.0713 4.0290 1.9446 8.0449 No 2.0141 4.0280 2.0320 8.0742 No 2.0092 4.0883 1.9087 8.0063 No 2.0901 4.1540 2.0707 8.3147 Yes 2.0896 4.1846 1.9447 8.2190 Yes 2.0933 3.9623 2.0414 8.0970 No 2.0402 3.9034 2.0162 7.9598 No 2.0796 3.8907 1.9083 7.8785 No 2.0083 4.0049 2.0102 8.0234 No 2.0715 3.9767 2.0328 8.0810 No 2.0140 3.9736 1.8914 7.8789 No 2.0003 4.0509 2.0601 8.1113 No 2.0201 4.1012 2.0496 8.1709 No 2.0137 3.9349 2.0795 8.0282 No 2.0558 4.1499 1.9653 8.1709 No 2.0638 3.8985 1.9947 7.9569 No 2.0786 3.9350 1.9397 7.9533 No 2.0439 4.0264 2.0497 8.1200 No 2.0910 3.9228 1.9742 7.9880 No 2.0537 3.8371 1.9755 7.8663 No 2.0036 3.8633 2.0163 7.8831 No 2.0406 3.9129 2.0064 7.9600 No 2.0188 3.9640 2.1019 8.0847 No 2.0175 4.0171 1.9505 7.9852 No 2.0674 4.0868 2.0032 8.1574 No 2.0917 3.6863 1.9705 7.7485 No 2.0114 4.0419 1.9679 8.0211 No 2.0812 4.0046 2.0380 8.1238 No 2.0146 3.9268 2.0409 7.9823 No 2.0472 3.9584 2.0229 8.0286 No 2.0177 3.9987 2.0481 8.0646 No 2.0508 3.9839 2.0155 8.0502 No 2.0187 3.9660 2.0895 8.0742 No 2.0617 4.1108 2.0556 8.2281 Yes 2.0991 3.9559 2.0253 8.0804 No 2.0177 3.8278 1.9462 7.7917 No 2.0289 3.8871 2.0624 7.9785 No 2.0662 3.8615 1.9605 7.8882 No 2.0753 3.9768 1.9899 8.0421 No 2.0330 4.1203 1.9310 8.0843 No 2.0103 4.0155 1.9878 8.0136 No 2.0611 3.9509 2.0075 8.0196 No 2.0094 4.1416 1.9390 8.0900 No 2.0662 3.9803 2.0410 8.0875 No 2.0299 4.0532 1.9098 7.9929 No 2.0697 4.0532 1.9118 8.0347 No 2.0086 3.8794 2.0060 7.8939 No 2.0139 3.9563 2.0533 8.0235 No 2.0922 4.0760 2.0332 8.2014 Yes 2.0438 3.9470 1.9497 7.9406 No 2.0702 3.9218 2.0125 8.0045 No 2.0749 3.9582 1.8870 7.9201 No 2.0778 4.1028 2.0390 8.2196 Yes 2.0618 4.0481 1.9698 8.0796 No 2.0507 4.0310 1.9869 8.0685 No 2.0564 3.9544 2.0327 8.0436 No 2.0866 4.0281 2.0053 8.1200 No 2.0092 3.9365 1.9461 7.8919 No 2.0851 3.9118 1.9773 7.9742 No 2.0270 3.7880 1.9935 7.8085 No 2.0412 3.9880 2.0252 8.0544 No 2.0837 4.0434 2.0237 8.1509 No 2.0361 3.8794 1.9796 7.8950 No 2.0828 3.8044 2.0114 7.8986 No 2.0509 3.9908 1.9786 8.0203 No 2.0136 3.9679 2.0165 7.9980 No 2.0998 3.9299 2.0221 8.0518 No 2.0419 4.0039 2.0334 8.0791 No 2.0914 4.0099 1.9973 8.0987 No 2.0315 3.7602 1.9577 7.7493 No 2.0476 3.9312 1.9866 7.9654 No 2.0324 3.9478 2.0882 8.0683 No 2.0030 3.9285 2.0176 7.9491 No 2.0938 3.9774 1.9953 8.0665 No 2.0306 4.0188 2.1037 8.1530 No 2.0903 4.0329 1.9713 8.0944 No 2.0590 4.0095 2.0406 8.1091 No 2.0858 4.1884 2.0073 8.2816 Yes 2.0263 4.0178 1.9690 8.0131 No 2.0326 3.9867 2.0779 8.0972 No 2.0096 3.9058 2.0038 7.9192 No 2.0039 3.9372 1.9881 7.9292 No 2.0549 4.0442 2.0806 8.1797 No 2.0210 3.9819 1.8949 7.8978 No 2.0528 4.0457 2.0169 8.1153 No 2.0549 4.0110 1.9286 7.9945 No 2.0434 3.8670 1.9254 7.8358 No 2.0822 4.0093 1.9214 8.0129 No 2.0360 4.0860 2.0589 8.1809 No 2.0636 3.8542 1.9980 7.9159 No 2.0655 4.1339 2.0134 8.2129 Yes 2.0002 3.9797 1.9997 7.9797 No 2.0417 4.0006 1.9853 8.0276 No 2.0291 4.1202 2.0051 8.1544 No 2.0358 4.1532 2.0139 8.2029 Yes 2.0466 3.9731 1.9793 7.9991 No 2.0595 3.8287 1.9566 7.8448 No 2.0198 4.1809 1.9924 8.1931 No 2.0861 3.9492 2.0972 8.1325 No 2.0636 3.9559 2.0885 8.1080 No 2.0988 4.0072 1.9973 8.1034 No 2.0490 3.9707 1.9627 7.9824 No 2.0023 3.9008 1.9821 7.8853 No 2.0666 3.9115 1.9979 7.9759 No 2.0444 3.9699 1.9299 7.9442 No 2.0205 3.9873 1.9752 7.9829 No 2.0497 3.9672 1.9735 7.9904 No 2.0807 4.0038 2.0099 8.0945 No 2.0081 3.6874 2.0225 7.7180 No 2.0854 3.9630 1.9189 7.9672 No 2.0644 4.0435 1.8646 7.9725 No 2.0785 4.0409 1.9501 8.0695 No 2.0801 3.9258 1.9826 7.9885 No 2.0009 3.9782 1.9458 7.9248 No 2.0402 3.8750 2.0757 7.9910 No 2.0320 4.2988 2.0448 8.3756 Yes 2.0332 4.0815 2.0934 8.2080 Yes 2.0313 3.9623 2.0484 8.0421 No 2.0878 3.9379 2.0169 8.0426 No 2.0479 4.1802 1.9921 8.2202 Yes 2.0815 3.9658 2.0406 8.0879 No 2.0823 4.0683 2.0436 8.1942 No 2.0954 3.8759 2.0529 8.0241 No 2.0982 3.8867 2.0696 8.0545 No 2.0496 3.9809 1.9456 7.9761 No 2.0080 3.8796 2.0249 7.9126 No 2.0677 4.1015 2.0081 8.1772 No 2.0149 3.8973 1.9788 7.8910 No 2.0519 4.0070 1.9861 8.0450 No 2.0837 4.0318 2.1211 8.2365 Yes 2.0731 4.0888 2.0371 8.1990 No 2.0622 4.1100 2.0042 8.1764 No 2.0385 3.9194 2.0615 8.0193 No 2.0818 3.8849 2.0079 7.9747 No 2.0755 4.0430 2.0394 8.1578 No 2.0528 3.9352 1.9998 7.9877 No 2.0081 3.8780 1.9919 7.8781 No 2.0451 3.9555 1.9651 7.9657 No 2.0798 4.1083 2.0623 8.2503 Yes 2.0238 4.0486 1.9926 8.0650 No 2.0433 4.0062 2.0200 8.0695 No 2.0945 4.0880 2.0523 8.2348 Yes 2.0691 4.0847 1.8847 8.0386 No 2.0381 3.8113 2.1275 7.9770 No 2.0688 3.7463 1.9187 7.7338 No 2.0645 4.0871 1.9566 8.1081 No 2.0616 4.0196 1.9750 8.0562 No 2.0263 3.8881 1.9899 7.9042 No 2.0890 3.9157 2.1239 8.1287 No 2.0058 3.9625 1.9571 7.9253 No 2.0651 4.0458 1.9853 8.0963 No 2.0346 3.9387 1.9656 7.9390 No 2.0046 4.0128 1.9914 8.0087 No 2.0459 4.0779 2.0620 8.1858 No 2.0578 4.0241 2.1033 8.1852 No 2.0962 4.1673 1.9636 8.2270 Yes 2.0639 3.8265 2.0166 7.9069 No 2.0485 3.8894 1.9815 7.9195 No 2.0731 4.0670 2.0402 8.1804 No 2.0884 4.0898 1.9284 8.1066 No 2.0509 4.0305 2.0241 8.1054 No 2.0615 3.9991 1.9683 8.0290 No 2.0167 4.0213 1.9852 8.0231 No 2.0950 4.1311 2.0331 8.2592 Yes 2.0632 3.9943 1.9403 7.9978 No 2.0961 4.0832 1.9657 8.1450 No 2.0936 3.9495 2.0404 8.0835 No 2.0362 3.8872 2.0605 7.9839 No 2.0835 4.0929 1.9757 8.1521 No 2.0249 3.8743 2.0235 7.9228 No 2.0743 3.8830 2.0343 7.9916 No 2.0838 3.8984 1.9505 7.9326 No 2.0965 3.9543 1.9401 7.9909 No 2.0427 4.1575 1.9265 8.1267 No 2.0771 3.9742 1.9582 8.0096 No 2.0264 4.0071 2.0874 8.1208 No 2.0564 4.1019 1.9747 8.1330 No 2.0777 4.0439 2.0238 8.1454 No 2.0953 4.0451 2.0922 8.2327 Yes 2.0002 3.9519 1.9849 7.9370 No 2.0561 4.0475 1.9753 8.0789 No 2.0959 3.9854 2.0119 8.0932 No 2.0471 4.1173 1.9704 8.1348 No 2.0518 3.8039 2.0588 7.9145 No 2.0022 4.1270 2.0547 8.1840 No 2.0882 4.0826 2.0419 8.2127 Yes 2.0767 4.0578 1.9166 8.0511 No 2.0476 3.8759 2.0000 7.9235 No 2.0492 4.1733 2.0785 8.3010 Yes 2.0814 3.9698 2.0049 8.0561 No 2.0843 4.0229 2.0033 8.1105 No 2.0958 4.0862 1.9328 8.1148 No 2.0949 3.9482 2.0323 8.0754 No 2.0629 4.1172 2.0012 8.1814 No 2.0135 4.1921 1.9724 8.1780 No 2.0974 4.0367 1.9891 8.1232 No 2.0918 3.7416 2.0908 7.9241 No 2.0610 4.0324 1.9365 8.0298 No 2.0739 4.0405 1.9499 8.0644 No 2.0902 3.9547 2.0076 8.0525 No 2.0754 3.9151 1.9629 7.9533 No 2.0701 4.2354 1.9778 8.2834 Yes 2.0275 4.0717 1.8980 7.9972 No 2.0033 3.9583 2.0074 7.9690 No 2.0653 3.9729 2.0495 8.0877 No 2.0626 3.7831 2.0129 7.8585 No 2.0158 4.1383 1.9472 8.1014 No 2.0860 3.8117 2.0125 7.9102 No 2.0392 3.9679 2.0328 8.0400 No 2.0766 3.9682 1.8787 7.9235 No 2.0582 4.0033 2.0932 8.1547 No 2.0283 3.9862 2.0383 8.0527 No 2.0359 4.0866 2.0748 8.1972 No 2.0225 3.9048 1.9655 7.8927 No 2.0965 3.9918 2.0690 8.1572 No 2.0368 4.0542 2.0364 8.1273 No 2.0873 3.9251 1.9202 7.9325 No 2.0960 4.0214 2.0565 8.1738 No 2.0165 3.9623 1.9704 7.9493 No 2.0840 3.9206 1.9745 7.9791 No 2.0359 4.0155 2.0079 8.0593 No 2.0408 4.1620 1.9009 8.1037 No 2.0238 3.9601 2.0221 8.0060 No 2.0942 3.9878 2.0759 8.1580 No 2.0382 4.0995 1.9434 8.0812 No 2.0504 3.9257 1.9694 7.9455 No 2.0005 4.1090 1.9430 8.0526 No 2.0831 4.0459 2.0587 8.1877 No 2.0082 3.9325 2.0196 7.9603 No 2.0490 3.9987 2.0313 8.0789 No 2.0243 3.9546 1.9770 7.9560 No 2.0163 3.9402 1.9952 7.9517 No 2.0044 3.9137 2.0132 7.9313 No 2.0442 3.9633 1.9520 7.9594 No 2.0740 4.1475 2.1266 8.3481 Yes 2.0029 3.8458 2.1127 7.9614 No 2.0127 4.0024 1.8951 7.9101 No 2.0897 4.1633 1.9411 8.1941 No 2.0032 4.1019 1.9249 8.0301 No 2.0882 3.9521 1.9984 8.0387 No 2.0292 3.9990 2.0611 8.0893 No 2.0503 3.9897 2.0509 8.0909 No 2.0077 4.0657 2.0033 8.0766 No 2.0632 4.0921 1.9615 8.1168 No 2.0953 4.1400 1.9705 8.2057 Yes 2.0095 4.0672 1.9465 8.0232 No 2.0663 3.8460 2.0084 7.9207 No 2.0552 4.0513 1.9825 8.0890 No 2.0880 4.0354 2.0596 8.1830 No 2.0092 3.8698 2.0310 7.9099 No 2.0824 4.1322 1.9159 8.1305 No 2.0152 3.9473 2.0364 7.9988 No 2.0199 3.7903 1.9856 7.7958 No 2.0641 4.0203 1.9843 8.0686 No 2.0049 3.7878 2.0380 7.8307 No 2.0686 4.2248 1.9589 8.2523 Yes 2.0505 4.0772 1.9774 8.1051 No 2.0397 3.8990 1.9826 7.9213 No 2.0556 4.0435 2.0240 8.1231 No 2.0437 3.7688 1.8993 7.7118 No 2.0625 3.9872 2.0419 8.0916 No 2.0356 4.1539 2.0036 8.1930 No 2.0432 4.1622 1.9843 8.1897 No 2.0441 3.9518 2.0081 8.0041 No 2.0066 3.8390 2.0366 7.8822 No 2.0636 4.0607 1.9956 8.1199 No 2.0894 3.9456 1.9436 7.9786 No 2.0813 4.0139 1.9783 8.0735 No 2.0674 3.9263 1.9663 7.9600 No 2.0629 3.9532 1.9302 7.9462 No 2.0478 4.0545 2.0510 8.1534 No 2.0319 3.8558 1.9633 7.8511 No 2.0539 3.9742 1.9526 7.9806 No 2.0412 4.0278 1.9497 8.0188 No 2.0418 4.0123 1.8795 7.9337 No 2.0357 3.8971 2.0521 7.9850 No 2.0670 3.8955 1.9523 7.9147 No 2.0840 3.8286 1.9236 7.8362 No 2.0003 3.9524 1.9479 7.9006 No 2.0006 3.9430 1.9504 7.8940 No 2.0484 4.0036 1.9434 7.9954 No 2.0209 3.9837 1.9721 7.9767 No 2.0201 3.9528 2.0609 8.0338 No 2.0289 4.0833 2.0043 8.1165 No 2.0628 3.9406 2.0285 8.0318 No 2.0914 4.0483 2.0795 8.2192 Yes 2.0316 4.0366 1.9187 7.9869 No 2.0323 4.0138 2.0027 8.0488 No 2.0171 4.1634 2.0284 8.2088 Yes 2.0998 3.9822 2.0617 8.1437 No 2.0972 3.9579 2.0671 8.1222 No 2.0492 3.8391 1.9658 7.8541 No 2.0700 4.0311 1.9915 8.0926 No 2.0994 3.8966 2.0197 8.0157 No 2.0197 3.9137 1.9257 7.8591 No 2.0313 4.0490 2.0572 8.1376 No 2.0338 3.9474 2.0847 8.0660 No 2.0980 4.0795 2.0362 8.2136 Yes 2.0897 3.8427 1.9115 7.8438 No 2.0155 3.9890 1.8763 7.8808 No 2.0239 4.1257 2.0050 8.1546 No 2.0240 3.9645 2.0298 8.0183 No 2.0490 3.8373 1.8993 7.7856 No 2.0446 4.1280 1.9962 8.1688 No 2.0565 4.0122 2.0726 8.1412 No 2.0447 4.0450 1.9550 8.0448 No 2.0992 4.0356 2.0780 8.2129 Yes 2.0549 4.0125 1.9798 8.0472 No 2.0493 3.9753 2.0499 8.0744 No 2.0763 4.0188 2.0083 8.1033 No 2.0329 4.1389 1.9644 8.1363 No 2.0949 4.0431 2.0232 8.1611 No 2.0280 4.0046 1.9974 8.0301 No 2.0774 4.1083 2.0302 8.2158 Yes 2.0159 3.8425 1.9991 7.8575 No 2.0911 4.0124 2.0403 8.1438 No 2.0916 3.8491 1.9673 7.9080 No 2.0664 3.9540 2.0528 8.0733 No 2.0985 3.9446 1.9825 8.0256 No 2.0266 3.9159 2.0046 7.9470 No 2.0391 3.9888 2.0107 8.0386 No 2.0526 4.1921 1.9639 8.2086 Yes 2.0842 3.9605 2.0664 8.1111 No 2.0474 4.0316 1.9993 8.0783 No 2.0118 4.0173 2.1114 8.1404 No 2.0221 4.2103 1.9204 8.1528 No 2.0335 4.0723 2.0425 8.1483 No 2.0639 4.0107 1.9906 8.0652 No 2.0534 4.0629 1.9746 8.0909 No 2.0701 3.9669 2.0630 8.1001 No 2.0315 4.1744 1.9985 8.2044 Yes 2.0605 4.0870 2.0866 8.2340 Yes 2.0421 4.0318 1.9734 8.0474 No 2.0183 4.1770 1.9251 8.1204 No 2.0966 3.9909 2.0398 8.1273 No 2.0815 3.9450 2.0566 8.0831 No 2.0957 4.0514 1.9870 8.1342 No 2.0094 4.0395 1.9935 8.0424 No 2.0594 3.9351 1.8738 7.8682 No 2.0075 4.0088 2.0642 8.0806 No 2.0060 3.9677 2.0726 8.0463 No 2.0195 4.0051 2.1139 8.1386 No 2.0892 4.0201 1.9257 8.0350 No 2.0879 4.1596 1.9961 8.2436 Yes 2.0021 4.0241 2.0037 8.0299 No 2.0780 4.0803 2.0019 8.1601 No 2.0968 3.8853 2.0272 8.0093 No 2.0458 4.0844 1.9654 8.0956 No 2.0993 4.1269 1.9418 8.1680 No 2.0356 3.9193 1.8944 7.8494 No 2.0906 3.8423 1.9634 7.8963 No 2.0208 4.1160 2.0764 8.2132 Yes 2.0331 4.0495 1.9440 8.0266 No 2.0732 4.1107 1.9217 8.1056 No 2.0162 4.0541 2.0768 8.1471 No 2.0646 4.1585 1.9636 8.1867 No 2.0346 4.1125 1.9742 8.1212 No 2.0888 4.1547 1.9958 8.2392 Yes 2.0549 3.9727 2.0177 8.0454 No 2.0557 4.1504 1.9721 8.1781 No 2.0485 3.9866 2.0557 8.0908 No 2.0560 3.9935 2.0915 8.1410 No 2.0121 3.9371 1.9877 7.9370 No 2.0493 3.8440 2.0213 7.9146 No 2.0476 3.9533 1.9793 7.9802 No 2.0937 4.0430 2.0670 8.2037 Yes 2.0710 4.0143 2.1195 8.2049 Yes 2.0263 4.0401 1.9451 8.0115 No 2.0462 4.1137 2.0311 8.1910 No 2.0369 4.0545 2.0345 8.1258 No 2.0421 3.9086 1.9134 7.8641 No 2.0590 3.8175 1.9676 7.8440 No 2.0667 4.0083 1.9963 8.0713 No 2.0503 4.0571 1.9940 8.1014 No 2.0848 3.8358 2.0036 7.9242 No 2.0578 3.8857 1.9402 7.8837 No 2.0616 4.1882 2.0384 8.2882 Yes 2.0751 4.0816 1.9876 8.1443 No 2.0304 3.8405 2.0038 7.8747 No 2.0153 3.9172 1.9465 7.8791 No 2.0442 3.8481 2.0484 7.9407 No 2.0488 4.0583 1.9420 8.0491 No 2.0839 3.8563 2.0490 7.9892 No 2.0127 3.9861 1.9921 7.9909 No 2.0312 3.9540 1.9945 7.9798 No 2.0900 3.9604 1.9747 8.0251 No 2.0336 4.1698 1.9893 8.1927 No 2.0048 4.0364 1.9956 8.0368 No 2.0507 4.1217 2.0160 8.1884 No 2.0873 3.9097 1.9868 7.9838 No 2.0450 4.0990 1.9731 8.1171 No 2.0489 4.0924 2.0076 8.1490 No 2.0177 4.0841 2.0118 8.1136 No 2.0846 3.9319 1.9828 7.9993 No 2.0695 4.0745 2.0549 8.1989 No 2.0932 3.8500 1.9448 7.8880 No 2.0317 4.0424 2.0611 8.1351 No 2.0016 4.0458 2.0485 8.0959 No 2.0435 4.2005 1.9463 8.1904 No 2.0905 3.9493 2.1345 8.1743 No 2.0978 3.9716 2.1122 8.1816 No 2.0820 3.8961 1.9557 7.9337 No 2.0081 4.0560 1.9138 7.9779 No 2.0524 3.9690 2.0241 8.0455 No 2.0265 3.8892 2.0713 7.9870 No 2.0081 4.0389 2.0537 8.1007 No 2.0260 3.8765 1.9508 7.8533 No 2.0107 3.8857 1.9636 7.8599 No 2.0129 3.8966 2.0171 7.9266 No 2.0744 4.0256 1.9898 8.0897 No 2.0249 4.1341 1.9423 8.1013 No 2.0998 4.0909 1.9675 8.1582 No 2.0504 4.0357 1.9761 8.0621 No 2.0588 4.1187 2.0185 8.1960 No 2.0448 4.0013 1.8840 7.9301 No 2.0279 4.0440 2.0395 8.1114 No 2.0815 3.9496 2.0086 8.0398 No 2.0842 4.0862 1.9586 8.1291 No 2.0171 3.9030 2.0684 7.9886 No 2.0506 4.0689 2.0295 8.1489 No 2.0382 4.0731 2.0137 8.1250 No 2.0088 4.0084 1.9453 7.9626 No 2.0552 4.1274 1.9470 8.1297 No 2.0138 3.8569 1.9837 7.8543 No 2.0753 3.9855 1.9798 8.0406 No 2.0380 4.3079 2.0362 8.3821 Yes 2.0821 4.0879 1.9377 8.1078 No 2.0817 3.8670 2.0668 8.0155 No 2.0511 3.8830 2.0095 7.9436 No 2.0964 4.1036 1.9583 8.1584 No

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