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Part $1$

Refer to Table S$6\mathrm{.}1-$ Factors for Computing Control Chart Limits $(3$ sigma$)$LOADING$...$ for this problem.

Twelve$$ samples, each containing five$$ parts, were taken from a process that produces steel rods at Emmanual$$ Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results$$ were:

$$

Sample

Sample Mean$($in$.)$

Range$($in$.)$

Sample

Sample Mean$($in$.)$

Range$($in$.)$

$1$

$9\mathrm{.}602$

$0\mathrm{.}044$

$7$

$9\mathrm{.}603$

$0\mathrm{.}021$

$2$

$9\mathrm{.}602$

$0\mathrm{.}051$

$8$

$9\mathrm{.}607$

$0\mathrm{.}058$

$3$

$9\mathrm{.}589$

$0\mathrm{.}042$

$9$

$9\mathrm{.}595$

$0\mathrm{.}039$

$4$

$9\mathrm{.}606$

$0\mathrm{.}037$

$10$

$9\mathrm{.}601$

$0\mathrm{.}038$

$5$

$9\mathrm{.}597$

$0\mathrm{.}048$

$11$

$9\mathrm{.}601$

$0\mathrm{.}054$

$6$

$9\mathrm{.}599$

$0\mathrm{.}053$

$12$

$9\mathrm{.}604$

$0\mathrm{.}061$

Part $2$

For the given$$ data, the x double overbar $=$

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