Problem $10-25($Algo$)$

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

SAMPLE NUMBER

$1$ READINGS $($IN OHMS$)$

$1,1,085,1,098,1,020,970$

$2,974,974,975,995$

$3,977,1,079,971$

$3,977,1,019,971,995$

$4,1,025,987,980,1,014$

$5,1,025,987,980,1,014$

$6,1,002,988,1,008,1,020$

$6,1,008,987,981,1,027$

$7,976,992,991,987$

$8,1,019,1,009,999,1,009$

$9,1,026,985,1,021,988$

$10,1,022,977,1,005,1,028$

$11,1,020,1,023,981,1,015$

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

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

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

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

c$.$ Determine the UCL and LCL for a $\stackrel{}{x}$ chart.

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