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 6 kettles, all of which receive dye liquor from a common source. Past data show that pH varies according to a Normal distribution with μ = 4.86 and σ = 0.133. 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 6. 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:

Answer 1

Solution :

Given that,

= 4.86

= 0.133

The 3 - control limits for chart are given by : x 3/n

Smaller value = x - 3/n = 4.86 - 3 * 0.133 / 6 = 4.6397

Largest value = x + 3/n = 4.86 + 3 * 0.133 / 6 = 5.023