$7\mathrm{.}29.$ 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 $7$E$.10.$

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

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

$7\mathrm{.}30.$ Analyze the data in Exercise $7\mathrm{.}29$ using an average sample size.

$7\mathrm{.}31.$ Construct a standardized control chart for the data in Exercise $7\mathrm{.}29.$

$7\mathrm{.}32.$ Continuation of Exercise $7\mathrm{.}29.$ Note that in Exercise $7\mathrm{.}29$ 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 Exercise $7\mathrm{.}29.$ How easy would this method be to use in practice?