The unique colors of the cashmere sweaters your firm makes result from heating u

Question

The unique colors of the cashmere sweaters your 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 6 kettles, all of which receive dye liquor from a common source. Past data show that pH varies according to a Normal distribution with = 4.67 and = 0.141. 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 6. The mean pH x is compared with "control limits" given by the 99.7 part of the 689599.7 rule for normal distributions, namely x ± 3x. What are the numerical values of these control limits for x? (Round your answers to three decimal places.)

_____ (smaller value)

______ (larger value)

Explanation / Answer

Solution:

99.7% of data lie within three standard deviations of the mean.

= 4.67 ± 3(0.141) / 6
= 4.8 ± 0.1726

Lower control limit = 4.627

Upper control limit = 4.973

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