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

$12345$

$10\mathrm{.}4870\mathrm{.}4810\mathrm{.}4850\mathrm{.}5090\mathrm{.}484$

$20\mathrm{.}5010\mathrm{.}5050\mathrm{.}5170\mathrm{.}4900\mathrm{.}525$

$30\mathrm{.}4970\mathrm{.}4990\mathrm{.}5140\mathrm{.}4860\mathrm{.}516$

$40\mathrm{.}4960\mathrm{.}5050\mathrm{.}4850\mathrm{.}4830\mathrm{.}488$

$50\mathrm{.}4730\mathrm{.}5030\mathrm{.}5230\mathrm{.}4680\mathrm{.}487$

$60\mathrm{.}4740\mathrm{.}4830\mathrm{.}5060\mathrm{.}4810\mathrm{.}504$

$70\mathrm{.}4960\mathrm{.}5110\mathrm{.}4930\mathrm{.}4720\mathrm{.}497$

$80\mathrm{.}5230\mathrm{.}5050\mathrm{.}4940\mathrm{.}4730\mathrm{.}493$

$90\mathrm{.}4950\mathrm{.}5000\mathrm{.}5130\mathrm{.}5020\mathrm{.}501$

$100\mathrm{.}4940\mathrm{.}5010\mathrm{.}5170\mathrm{.}5090\mathrm{.}491$

$110\mathrm{.}4960\mathrm{.}4850\mathrm{.}4600\mathrm{.}4920\mathrm{.}486$

$120\mathrm{.}4840\mathrm{.}4600\mathrm{.}5110\mathrm{.}4970\mathrm{.}515$

$130\mathrm{.}5250\mathrm{.}5110\mathrm{.}4810\mathrm{.}5260\mathrm{.}513$

$140\mathrm{.}4880\mathrm{.}5220\mathrm{.}5060\mathrm{.}5070\mathrm{.}503$

$150\mathrm{.}4910\mathrm{.}5170\mathrm{.}4980\mathrm{.}5090\mathrm{.}509$

$160\mathrm{.}4720\mathrm{.}5050\mathrm{.}4700\mathrm{.}4810\mathrm{.}528$

$170\mathrm{.}4690\mathrm{.}4820\mathrm{.}5120\mathrm{.}4830\mathrm{.}497$

$180\mathrm{.}5160\mathrm{.}4850\mathrm{.}4810\mathrm{.}4840\mathrm{.}470$

$190\mathrm{.}5120\mathrm{.}5250\mathrm{.}4830\mathrm{.}4910\mathrm{.}495$

$200\mathrm{.}4980\mathrm{.}4930\mathrm{.}4710\mathrm{.}4970\mathrm{.}511$

Calculate the mean and range for the above samples.

Determine X$$ and R$$

Determine the UCL and LCL for an X$$

$-$chart

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