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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:

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Sample

Sample Mean $($in$.)$

Range $($in$.)$

Sample

Sample Mean $($in$.)$

$112\mathrm{.}304$

$212\mathrm{.}302$

$312\mathrm{.}293$

$412\mathrm{.}308$

$512\mathrm{.}299$

$612\mathrm{.}297$

$712\mathrm{.}301$

$812\mathrm{.}303$

$912\mathrm{.}297$

$1012\mathrm{.}303$

$1112\mathrm{.}301$

$1212\mathrm{.}304$

Range $($in$.)$

$10\mathrm{.}033$

$20\mathrm{.}041$

$30\mathrm{.}034$

$40\mathrm{.}051$

$50\mathrm{.}031$

$60\mathrm{.}036$

$70\mathrm{.}041$

$80\mathrm{.}034$

$90\mathrm{.}027$

$100\mathrm{.}029$

$110\mathrm{.}039$

$120\mathrm{.}047$

Part $2$

For the given data, the $=$

$$

enter your response here inches $($round your response to four decimal places$).$