The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one$-$hour intervals. Use three$-$sigma control limits$.$ Use Exhibit $13\mathrm{.}7.$

SAMPLE NUMBER OBSERVATIONS

$12345$

$10\mathrm{.}4860\mathrm{.}4990\mathrm{.}4930\mathrm{.}5110\mathrm{.}481$

$20\mathrm{.}4990\mathrm{.}5060\mathrm{.}5160\mathrm{.}4940\mathrm{.}529$

$30\mathrm{.}4960\mathrm{.}5000\mathrm{.}5150\mathrm{.}4880\mathrm{.}521$

$40\mathrm{.}4950\mathrm{.}5060\mathrm{.}4830\mathrm{.}4870\mathrm{.}489$

$50\mathrm{.}4720\mathrm{.}5020\mathrm{.}5260\mathrm{.}4690\mathrm{.}481$

$60\mathrm{.}4730\mathrm{.}4950\mathrm{.}5070\mathrm{.}4930\mathrm{.}506$

$70\mathrm{.}4950\mathrm{.}5120\mathrm{.}4900\mathrm{.}4710\mathrm{.}504$

$80\mathrm{.}5250\mathrm{.}5010\mathrm{.}4980\mathrm{.}4740\mathrm{.}485$

$90\mathrm{.}4970\mathrm{.}5010\mathrm{.}5170\mathrm{.}5060\mathrm{.}516$

$100\mathrm{.}4950\mathrm{.}5050\mathrm{.}5160\mathrm{.}5110\mathrm{.}497$

$110\mathrm{.}4950\mathrm{.}4820\mathrm{.}4680\mathrm{.}4920\mathrm{.}492$

$120\mathrm{.}4830\mathrm{.}4590\mathrm{.}5260\mathrm{.}5060\mathrm{.}522$

$130\mathrm{.}5210\mathrm{.}5120\mathrm{.}4930\mathrm{.}5250\mathrm{.}510$

$140\mathrm{.}4870\mathrm{.}5210\mathrm{.}5070\mathrm{.}5010\mathrm{.}500$

$150\mathrm{.}4930\mathrm{.}5160\mathrm{.}4990\mathrm{.}5110\mathrm{.}513$

$160\mathrm{.}4730\mathrm{.}5060\mathrm{.}4790\mathrm{.}4800\mathrm{.}523$

$170\mathrm{.}4770\mathrm{.}4850\mathrm{.}5130\mathrm{.}4840\mathrm{.}496$

$180\mathrm{.}5150\mathrm{.}4930\mathrm{.}4930\mathrm{.}4850\mathrm{.}475$

$190\mathrm{.}5110\mathrm{.}5360\mathrm{.}4860\mathrm{.}4970\mathrm{.}491$

$200\mathrm{.}5090\mathrm{.}4900\mathrm{.}4700\mathrm{.}5040\mathrm{.}512$

Calculate the mean and range for the above samples.

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

Determine X$=$

and R$$

$.$

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

Determine the UCL and LCL for an X$$

$-$chart.

Note: Do not round intermediate calculations. Round your answers to $3$ decimal places.

Determine the UCL and LCL for an R$-$chart.

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Do not round intermediate calculations. Round your answers to $3$ decimal places.

What comments can you make about the process?

multiple choice

The process is in statistical control.

The process is out of statistical control.