The percentage of potassium in a compound is expected to be within the specification limits of 18–35%. Samples of size 4 are selected, and the mean and range of 25 such samples are shown in Table 7-30. It is desirable for the process nonconformance to be within 1.5%. If the acceptable level of type I error is 0.05, find the modified control limits for the process mean.

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TABLE 7-30 Sample Sample Sample Average, X (%) Range, R (%) Sample Sample Average, X (%) Sample Range, R (%) 1 23.0 1.9 14 23.6 2.0 23 20.0 2.3 15 20.8 1.6 3 24.0 2.2 16 20.2 2.1 4 19.6 1.6 17 19.5 2.3 5 20.5 1.8 18 22.7 2.5 6 22.8 2.4 19 21.2 1.9 7 19.3 2.3 8 21.6 2.0 21 9 20.3 2.1 10 19.6 1.7 11 24.2 2.3 22222 20 22.9 2.2 20.6 2.1 23.5 2.4 23 21.6 1.8 24 22.6 2.3 12 21.9 1.8 25 20.5 2.2 13 20.6 1.8