The unique colors of cashmere sweaters a firm makes result from heating undyed yarn
in a kettle with a dye liquor. The pH (acidity) of the liquor is critical for regulating dye uptake and hence the final color. There are 5 kettles, all of which receive dye liquor from a common source. Past data show that pH varies according to a Normal distribution with μ = 4.35 and σ = 0.125. You use statistical process control to check the stability of the process. Twice each day, the pH of the liquor in each kettle is measured, giving a sample of size 5. The mean pH x is compared with “control limits” given by the 99.7 part of the 68−95−99.7 rule for normal distributions, namely
μx ± 3σx. What are the numerical values of these control limits for x? (Round to three decimal places.)
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