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

ID: 3208142 • Letter: T

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 = 4.12 and = 0.127. 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 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) (3.739 was wrong last time) ______   (larger value) (4.501 was wrong last time)

Explanation / Answer

ans=

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

4.12 ± 3(0.127) / 7

= 4.12 ± 0.381/ 2.6457

= 4.12 ± 0.144


A) Lower control limit = 3.976
B) Upper control limit = 4.264