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 $13\mathrm{.}7$

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 as in Exhibit $13\mathrm{.}7.$

$\backslash$table$[[$SAMPLE$,$READINGS,$($IN OHMS$)],[$NUMBER$,972,997,1032,972,,],[1,1024,1029,979,1024,,],[2,1002,1014,1007,1030,,],[3,981,1028,994,974,,],[4,983,1023,1025,988,,],[5,985,990,1019,979,,],[6,980,1002,995,991,,],[7,1011,1027,985,1004,,],[8,999,979,973,1022,,],[9,1019,983,974,996,,],[10,978,1018,979,984,,],[11,1002,974,985,984,,],[12,1030,1023,1004,1017,,],[13,995,998,997,1016,,],[14,973,983,1011,977,,],[15,,,,,,],[,,,,,,]]$

a$.$ Calculate the mean and range for the above samples.

Note: Round "Mean" to $2$ decimal places and "Range" to the nearest whole number.

$\backslash$table$[[$Sample Number,Mean,Range$],[1,993\mathrm{.}25,60],[2,1,014\mathrm{.}00,50],[3,1,013\mathrm{.}25,28],[4,994\mathrm{.}25,47],[5,1,004\mathrm{.}75,42],[6,993\mathrm{.}25,40],[7,992\mathrm{.}00,22],[8,1,006\mathrm{.}75,42],[9,993\mathrm{.}25,49],[10,993\mathrm{.}00,45],[11,989\mathrm{.}75,40],[12,986\mathrm{.}25,28],[13,1,018\mathrm{.}50,26],[14,1,001\mathrm{.}50,21],[15,986\mathrm{.}00,38]]$

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

Note: Round your answers to $3$ decimal places.

$\backslash$table$[[\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x}),1,003\mathrm{.}687$