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 = 4.28 and = 0.157. 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

we are given that = 4.28 and = 0.157 and N = 7

so we calculate the confidence interval as

mean +- 3 SD/sqrt(n)

so the values are 4.28 +-3*0.157/sqrt(7) , solving this equation as

4.28 +3*0.157/sqrt(7)

4.28 - 3*0.157/sqrt(7)

so the values are 4.101 and 4.458

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