Jamison Kovach Supply Company manufactures paper clips and other office products. Although$$ inexpensive, paper clips have provided the firm with a high margin of profitability. Sample size is $140.$ Results are given for the last $10$ samples.

$$

Sample

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Defectives

$4$

$7$

$3$

$6$

$5$

$5$

$5$

$4$

$2$

$11$

Part $2$

The type of control chart that is best to monitor this process is

p minus chartp$$chart

$.$

Part $3$

$$a$)$ Establish the control limits to include$99\mathrm{.}73\%$ of the random variation in defectives.

UCLp $=0\mathrm{.}0850\mathrm{.}085($enter your response as a number between $0$ and$1,$ rounded to three decimal$$ places$).$

Part $4$

LCLp $=0\mathrm{.}000\mathrm{.}00($enter your response as a number between $0$ and$1,$ rounded to three decimal$$ places$).$

Part $5$

$$b$)$ Has the process been in$$ control?

Based on the developed control$$ limits$,$ the number of defectives has been

IN$-$CONTROL

$.$

Part $6$

$$c$)$ If the sample size were $70$instead$,$ how would your limits and conclusions$$ change?

UCLp $=$ enter your response here $($enter your response as a number between $0$ and$1,$ rounded to three decimal$$ places$).$