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 $10\mathrm{.}13.$

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$)$

$11,0901,0961,002980$

$29749811,017994$

$39991,0289801,015$

$49999879951,006$

$51,0189711,018993$

$61,0109931,0241,017$

$79801,0131,028989$

$81,0079869721,027$

$91,0301,017997975$

$109791,0309701,003$

$119809871,0021,011$

$129899989741,007$

$131,0069951,0021,021$

$141,0071,0161,0051,004$

$159859971,003988$

Calculate the mean and range for the above samples.

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

Determine X$=$

and R$$

$.$

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

Determine the UCL and LCL for a X$$

chart.

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

What comments can you make about the process?

multiple choice

Process is out of statistical control

Process is in statistical control