Question: please show steps 5. A mean chart is used to maintain the diameter of plastic tubing. The process is known to have a standard deviation

please show steps please show steps 5. A mean chart is used to

5. A mean chart is used to maintain the diameter of plastic tubing. The process is known to have a standard deviation of 0.15cm. Five samples of three observations each are used to construct the mean chart. Sample 1 2 3 4 5 1 10.0 10.1 9.8 9.9 9.8 Observations (centimeters) 2 3 9.9 10.0 10.1 10.3 10.0 10.1 9.9 9.8 9.9 9.9 a) Compute x. (9.97) b) Compute three-sigma limits for an x-chart. (9.53, 10.23) c) Is the process in-control? Why or why not? (yes) d) Suppose that the process mean shifts to 10.2. (Assume that the standard deviation does not change.) What is probability of a Type II error? (That is, using the control limits calculated in part (b) what is the probability that the mean chart will indicate an in- control point in a sample of three observations.) (78.4%)

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