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 distributon with 4.49 and = 0.126. you use statstical 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 ± 3 what are the numerical values of these control limits for x? (Round your answers to three decimal places.) (smaller value) (larger value)

Explanation / Answer

For the normal distribution, the values within onestandard deviation of the mean account for 68.27% of the set; while within two standard deviations account for 95.45%; and within three standard deviations account for 99.73%.

Smaller value:

4.49 - 3 * 0.126/7 = 4.347

larger value:

4.49 + 3 * 0.126/7 = 4.633

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