PLEASE show work

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 3,200 customers, the retailer tried to find out if there are problems with the shipments. The survey response rate was 80%. The two tables in Hint at the end of the question can help you with some calculations. (a)[2] Twenty eight 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? (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: use the NORM.S.INV(*) function in Excel or the lookup table below to calculate sigma the levels; and use the Sigma-DPMO table below to find the number of errors. 0.99961 0.99414 0.98906 0.98711 0.98555 NORM.S.INV(av) 3.35935 2.52050 2.29253 2.22949 2.18476 Sigma Level 2.0 3.0 4.0 5.0 60 DPMO 308,537.5 66,8072 6,209.7 232.6 3.4 CV