ANSWER ALL PARTS Problem $10-29($Algo$)$

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 $10\mathrm{.}13.$

OBSERVATIONS

SAMPLE NUMBER $12345$

$10\mathrm{.}4650\mathrm{.}4940\mathrm{.}4930\mathrm{.}5110\mathrm{.}472$

$20\mathrm{.}4710\mathrm{.}5010\mathrm{.}5050\mathrm{.}4840\mathrm{.}515$

$30\mathrm{.}4720\mathrm{.}4930\mathrm{.}5160\mathrm{.}4930\mathrm{.}528$

$40\mathrm{.}4750\mathrm{.}5010\mathrm{.}4950\mathrm{.}4940\mathrm{.}492$

$50\mathrm{.}4810\mathrm{.}4980\mathrm{.}5230\mathrm{.}4570\mathrm{.}485$

$60\mathrm{.}4720\mathrm{.}4960\mathrm{.}5020\mathrm{.}4950\mathrm{.}505$

$70\mathrm{.}4940\mathrm{.}5020\mathrm{.}4940\mathrm{.}4710\mathrm{.}504$

$80\mathrm{.}5050\mathrm{.}4990\mathrm{.}4860\mathrm{.}4720\mathrm{.}487$

$90\mathrm{.}4720\mathrm{.}5010\mathrm{.}5070\mathrm{.}5040\mathrm{.}506$

$100\mathrm{.}4650\mathrm{.}5020\mathrm{.}5050\mathrm{.}5110\mathrm{.}485$

$110\mathrm{.}4950\mathrm{.}4950\mathrm{.}4560\mathrm{.}4940\mathrm{.}491$

$120\mathrm{.}4580\mathrm{.}4630\mathrm{.}5250\mathrm{.}5040\mathrm{.}529$

$130\mathrm{.}5160\mathrm{.}5020\mathrm{.}4950\mathrm{.}5210\mathrm{.}504$

$140\mathrm{.}4910\mathrm{.}5210\mathrm{.}5020\mathrm{.}4950\mathrm{.}508$

$150\mathrm{.}4930\mathrm{.}5050\mathrm{.}4870\mathrm{.}5110\mathrm{.}503$

$160\mathrm{.}4710\mathrm{.}5010\mathrm{.}4840\mathrm{.}4750\mathrm{.}525$

$170\mathrm{.}4810\mathrm{.}4810\mathrm{.}5080\mathrm{.}4730\mathrm{.}484$

$180\mathrm{.}5070\mathrm{.}4930\mathrm{.}4950\mathrm{.}4720\mathrm{.}484$

$190\mathrm{.}5010\mathrm{.}5390\mathrm{.}4940\mathrm{.}4850\mathrm{.}493$

$200\mathrm{.}5130\mathrm{.}4940\mathrm{.}4850\mathrm{.}5040\mathrm{.}502$

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 a X$$

$-$chart.

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

Determine the UCL and LCL for 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

Process is in statistical control.

Process is out of statistical control.