Sample sample std 11 10.18 0.16 sample average, x-bar deviation, s 12 9.85 0.15 10.19 0.15 13 9.82 0.06 2 9.8 0.12 14 10.18 0.34 10.12 0.18 15 9.96 0.11 4 10.54 0.19 16 9.57 0.09 U 9.86 0.14 17 10.14 0.12 9.45 0.09 18 10.08 0.15 10.06 0.16 19 9.82 0.09 10.13 0.18 20 10.15 0.12 9.82 0.14 10 10.17 0.13Hun-u IIIMIlUIUI!' vuuuuul 4U +a.v4.u Problem 1 (50 points) The thickness of sheet metal (in millimeters) used for making automobile bodies is a criticaltoquality characteristic of interest. Random samples of size 4 are taken every 30 minutes. The average and standard deviation are calculated for each sample and are shown in the table below for 20 samples. The specification limits are 9.95+/-O.3 mm. a. For a stable process. estimate the process mean and the process standard deviation. b. If the thickness of sheet metal exceeds the upper specification limit, it can be reworked. However, if the thickness is less than the lower specification limit, it cannot be used for its intended purpose and must be scrapped for other users. The cost of rework is $0.25 per linear foot, and the cost of scrap is $0.75 per linear foot. The rolling mills are 100 ft in length. The manufacturer has four such mills and run 80 batches on each mill daily. The plant operates 365 days a year. What is the annual cost of rework? What is the annual cost of scrap? c. If the manufacturer has the flexibility to change to process mean, should it be moved to 10.00. based on economic reasons? What is the financial impact of such an action