Using an injection molding process, a plastics company produces interchangeable

cell phone covers. After molding, the covers are sent through an intricate painting

process. Quality control engineers inspect the covers and record the paint

blemishes. The number of blemishes found in $20$ samples of $5$ covers are as follows:

$2,1,5,5,3,3,1,3,4,5,4,4,1,5,2,2,3,1,4,4.$

a$)$ Using all the data, compute trial control limits for a C control chart, construct

the chart, and plot the data. $(10).$ Paste all the relevant information in your

submission.

b$)$ Can we conclude that the process is in control using a C chart? $(5)$

c$)$ How would your conclusion in b$)$ change if you attempted this problem as a U

chart? $(10)$