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 5 kettles, all of which receive dye liquor from a common source. Past data show that pH varies according to a Normal distribution with = 4.68 and = 0.149. 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 5. 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.)

Explanation / Answer

Here mean=4.68 and sd=0.149

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard.

So 99.7 control limit=mu+/-3sd=4.68+/-3*0.149=(4.233,5.127)

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