$7.$ Construct the appropriate control chart for the observations listed below, using $2$ sigma limits$.$

Product number

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$11$

Number of defects

$7$

$3$

$3$

$5$

$6$

$5$

$4$

$4$

$3$

$1$

$3$

a$.$ Determine the upper and lower control limits$.$

b$.$Plot the control limits and the observations on the chart provided. Proper scaling, labeling and neatness counts.

c$.$Discuss the chart you have plotted. What conclusions and recommendations do you make from the chart and the data?