$4)$ A maintenance group improves the effectiveness of its repair work by monitoring the number of maintenance requests that require a second call to complete the repair. Twenty weeks of data are shown in Table below.

a$.$ Find trial control limits for this process.

b$.$ Design a control chart for controlling future production.

c$.$ Analyze the data using an average sample size.

d$.$ Construct a standardized control chart.

e$.$ Note that there are only four different sample sizes: n $=100,150,200,$ and $250.$ Prepare a control chart that has a set of limits for each possible sample size and show how it could be used as an alternative to the variable$-$width control limit method used in part $($a$).$ How easy would this method be to use in practice?