Question 21 - DPU and DPMO in Six Sigma

Please show all work in Excel is possible/applicable, thank you!

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 3,600 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] Thirty two 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). Sketch the sigma level. (b)[2] To achieve a calculated sigma level of 4.0, what would have been the number of errors? (show 4 decimal places) 1 (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? (show 4 decimal places) Can this number of errors actually 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 (2 decimal places)? 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 (rounded up) to have the number of errors in part (d). How many customers would the retailer need to contact (rounded up)