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 7 kettles, all of which receive dye liquor from a common source. Past data show that pH varies according to a Normal distribution with mu = 4.19 and sigma = 0.119. 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 7. 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 mu^-_x plusminus 3sigma^-_x. What are the numerical values of these control limits for x? (Round your answers to three decimal places.) (smaller value) (larger value)

Explanation / Answer

Here sample size =7

Mean = 4.19

Standard deviation = 0.119

for 3 sigma rule

Smaller control limit when Z = - 3

smalller control limit = - 3 s = 4.19 - 3 * 0.119/7 = 4.055

Upper control limit = + 3 s = 4.19 + 3 * 0.119/7 = 4.325

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