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 = 4.15and σ = 0.111. 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 your answers to three decimal places.)