Question $5(20$ points$)$

We purchase solenoids from a supplier, which arrive in containers of $5000$ each. One container arrives every day. Each day, we randomly select $250$ solenoids to test. For the first ten days, the fraction defective per container were: $0,0,0,0\mathrm{.}004,0\mathrm{.}008,0\mathrm{.}020,0\mathrm{.}004,0,0,0\mathrm{.}008.$

a$)$ Find the Center Line and Control Limits for a Fraction Nonconforming Control Chart.

b$)$ Is the process In Control or Out of Control?

c$)$ If it was Out of Control, assume any points outside the Limits were due to assignable causes, which were fixed, and the data removed. Do the remaining data show the process to be In Control or Out of Control?