At a local electronics manufacturer in College Corner, Ohio, resistors for electronic circuits are manufactured on a high$-$speed automated machine. The machine is set up to produce a large run of resistors of $1,000$ ohms each. Use Exhibit $10\mathrm{.}13.$

In a production setting, to set up the machine and to create a control chart to be used throughout the run, $15$ samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three$-$sigma control limits$.$

SAMPLE NUMBER READINGS $($IN OHMS$)$

$11010991985986$

$29959961009994$

$3990100310151008$

$4101510201009998$

$5101310191005993$

$699410019941005$

$79899929821020$

$81001986996996$

$9100698910051007$

$1099210071006979$

$119961006997989$

$1210199969911011$

$139819919891003$

$14999993988984$

$15101310021005992$

a$.$ Calculate the mean and range for the above samples. $($Round "Mean" to $2$ decimal places and "Range" to the nearest whole number.$)$

Sample Number Mean $?$ Range $?$e$.$ What comments can you make about the process?

The process is in statistical control.

The process is out of statistical control.

d$.$ Determine the UCL and LCL for $R-$chart. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to

$3$ decimal places.$)$

process?

The process is out of statistical control.

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

b$.$ Determine X$=$

and R$$

$.($Round your answers to $3$ decimal places.$)$

X$=$

R$$

c$.$ Determine the UCL and LCL for a X$$

chart. $($Round your answers to $3$ decimal places.$)$

UCL

LCL

d$.$ Determine the UCL and LCL for R$-$chart. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to $3$ decimal places.$)$

UCL

LCL

e$.$ What comments can you make about the process?

multiple choice

The process is in statistical control.? The processs is not?b$.$ Determine and ${?}^{(})\frac{\stackrel{}{x}}{b}ar(R).($Round your answers to $3$ decimal places.$)$

$\frac{\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})}{(\frac{?}{\text{b}\text{a}\text{r}}(R))}$

c$.$ Determine the UCL and LCL for a $\stackrel{}{x}$ chart. $($Round your answers to $3$ decimal places.$)$

UCL

LCL

d$.$ Determine the UCL and LCL for $R-$chart. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to

$3$ decimal places.$)$

UCL

LCL

e$.$ What comments can you make about the process?

The process is in statistical control.

The process is out of statistical control.