0.–/0.5 points MIntroStat8 5.E.523.XP. Ask Your Teacher My Notes Question Part P
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Question
0.–/0.5 points MIntroStat8 5.E.523.XP. Ask Your Teacher My Notes Question Part Points Submissions Used 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 = 4.98 and = 0.155. 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.)
a) smaller value b) bigger value
Explanation / Answer
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 = 4.98 and = 0.155. 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.)
x =0.155/sqrt(7) =0.0586
a) smaller value: 4.98-3*0.0586 = 4.8042
=4.804 ( rounded to 3 decimals)
b) bigger value: 4.98+3*0.0586 = 5.1558
=5.156 ( rounded to 3 decimals)
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