The required length of a machined part is specified with an equal bilateral tolerance of 6" 0.025. The process is currently averaging 5.989 with a standard deviation of 0.010. A1. What proportion of the process output is below the lower spec limit? A2. What proportion of the process output is above the upper spec limit? A3. If a sample of 12 parts is taken from the process for inspection, what is the probability that all the parts will be within the spec limits? (Use basic probability concepts.)

A4. If a sample of 12 parts is taken from the process for inspection, what is the probability that exactly 2 parts will be outside the specification limits? (binomial)

1.4843 0.9096 1.3207 0.4463 2.2450 3.7243 14.4315 3.3412 1.1011 2.3930 3.1745 0.9239 1.8494 0.7575 14.1088 2.1108 1.6849 4.6513 6.8514 2.0443 6.7555 0.6189 4.6081 0.7298 3.0769 0.4739 2.6664 2.1680 6.2741 11.0464 4.0663 0.5478 4.3596 5.8468 5.2169 3.8970 0.4641 2.2014 4.4191 3.2123 4.9260 5.2472 2.7892 3.1010 1.1126 0.8273 2.4775 13.2282 1.5493 1.7354 8.6275 7.3476 14.0542 9.3032 2.3077 0.2511 0.8826 6.0742 14.9822 2.2147 0.3772 25.8349 1.9368 1.1865 6.7844 2.0892 15.3702 5.4567 3.2150 0.9439 4.3568 6.3036 5.5650 6.8353 0.9116 9.1773 1.6797 22.3835 1.3339 2.6362 5.0961 2.5294 0.7818 1.7036 11.6246 2.0515 1.6684 2.2074 0.9334 6.7380 1.3091 5.1495 0.6777 3.0205 0.7981 8.4695 5.6766 1.6523 0.7814 23.0395 6.9254 4.8698 3.2184 5.3469 0.8548 6.6593 2.1890 1.4233 2.7050 19.9173 4.2858 4.5415 0.8604 3.1344 1.7853 2.6566 4.3012 1.0449 1.1654 5.2593 10.7603 0.6851 25.2889 2.4681 0.6240 1.0213 2.9757 2.6224 3.6449 0.8954 4.5939 1.3287 0.4986 6.7579 2.8128 1.4155 1.8688 5.4343 19.7232 3.6372 1.1520 2.5977 1.5891 2.0444 1.0761 1.0431 1.9257 1.5585 4.0447 2.4646 1.2569 4.2626 2.6391 2.6073 3.3261 1.1283 9.0419 1.0585 12.6092 21.8483 2.5022 8.0093 6.5787 1.5155 5.1838 8.5427 4.4940 0.5025 0.4148 8.0726 0.9308 3.0937 7.8877 3.9956 3.1051 5.6095 2.5118 12.3213 1.3620 2.9462 1.2144 13.6168 15.9290 0.9214 6.2098 0.9113 7.5521 0.7909 3.9306 3.5043 7.0428 3.0392 1.6223 47.6987 2.1480 1.9860 9.5393 1.6194 4.0660 3.3398