A firm that manufactures grape juice has a machine that automatically fills bottles. The mean of the process is assumed to be the machine's setting. The process variation (standard deviation) is 1.2 oz. (Assume that the process has a normal distribution.)

B1. Customers get unhappy if the actual level is less than 36 oz but do not mind if it is greater than 36 oz. If you set the machine at 37 oz. what % of the time would the bottle contain less than 36 oz.?

B2. The bottle will actually hold 40 oz. If you set the machine to 38, what percent of the time will the bottles overflow?

B3. If 10 bottles from this process (setting at 38) are filled, what is the probability that at least one will have overflowed? (Use basic probability concepts.)

B4. If 15 bottles from this process (setting at 38) are filled, what is the probability that exactly 3 will have overflowed? (binomial)

B5. With the machine set at 38 oz., how big would the bottle have to be not to overflow 99.8% of the time?

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