Question

The unique colors of the cashmere sweaters your firm makes result from heating undyed yarn in...

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 μ = 4.11 and σ = 0.116. 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

μx ± 3σx.

What are the numerical values of these control limits for x? (Round your answers to three decimal places.)

------------------------------    (smaller value)
----------------------------- (larger value)

Homework Answers

Answer #1

Solution :

Given that,

= 4.11

= 0.116

P( - 3< X < + 3) = 99.7%

P(4.11 - 3 * 0.116 < X < 4.11 + 3 * 0.116) = 99.7%

P(3.762 < X < 4.458) = 99.7%

The numerical values of these control limits for x are :

3.762

4.458

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