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 = 4.64 and = 0.128. 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)

______(larger value)

Explanation / Answer

mean-3 sd=lower limit

mean=4.64

smaple size=n=7

sd of X bar=0.128/sqrt(7)

=0.04837945

4.64-3*(0.04837945)= 4.495

and

4.64+3(0.04837945)=upper limit

4.785138=upper limtit

upper limit=4.785

ANSWER:

4.256(smaller value)

AND 4.785(upper limtit)

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