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4) The sample mean and range for samples of size 5 are given in the table 2. The specification on this product has been established to be 55+2. a) Construct a modified control chart with three sigma limits. Assume that if the fraction of nonconforming units is as large as 1%, the process is unacceptable. b) Suppose that if the true process fraction nonconforming is as large as 1%, we would like an acceptance control chart to detect this out-of-control condition with probability 0.9. Construct this acceptance control chart. Sample R 1 54.9 1.7 2 55.3 1.5 3 55.0 1.3 4 55.1 0.5 5 55.1 0.9 6 54.8 1 1.7 7 54.8 1.0 8 0.6 9 54.8 0.7 10 54.9 1.6 11 55.1 1.7 12 55.1 2.2 13 55.1 1.2 14 55.1 1.8 15 54.8 1.1 16 55.0 0.6 17 55.0 1.4 18 54.9 1.2 19 55.3 1.7 20 54.9 1.7