Please help a-e

QUESTION 21 (10 points) - DPU and DPMO in Six Sigma An online retailer carried out a random survey on shipments done by its Order Fulfillment Department. In contacting 1,875 customers, the retailer tried to find out if there are problems with the shipments. The survey response rate was 75%. The two tables in Hint at the end of the question can help you with some calculations. (a)[2] Twenty one shipments were found with problems, and each of those shipments is considered an error. Find DPU (7 decimal places), EPMO (1 decimal place), and the calculated sigma level of the fulfillment service (2 decimal places). (b)[2] To achieve a calculated sigma level of 4.0, what would have been the number of errors? (c)[2] Assume that the fulfillment service is actually at 5.0 sigma (the underlying sigma level). What would have been the theoretical number of errors? Can this number of errors happen? 1 (d) [2] This is a continuation of part (c). If there are errors, what is the lowest possible number of errors? If this lowest number of errors does happen, what would be the calculated sigma level? Would this calculated sigma level be a wrong indication of the underlying sigma level of 5.0? (e)[2] Given the underlying sigma level of 5.0, find the smallest sample size to have the number of errors in part (d). How many customers would the retailer need to contact? Hint: you can use some lookup values in the two tables below for your calculations. 0.99947 0.99360 0.98880 0.98613 0.98347 NORM.S.INV(av) 3.27233 2.48929 2.28352 2.20104 2.13127 Sigma Level 2.0 3.0 4.0 5.0 6.0 66807.2 6209.7 av DPMO 308537.5 232.6 3.4