Problem: Using four samples of $200$ credit card statements each, an auditor found the following number of erroneous statements in each sample:

Sample

$1234$

Number of errors $4259$

a$.$ Determine the proportion of defectives in each sample.

Sample Number of errors Proportion defective

$14$

$22$

$35$

$49$

b$.$ Estimate the proportion of defectives $($mean defectives$)$ and standard deviation of the sampling distribution $(\backslash$sigma $\_$p$)$ for this process?

c$.$ Construct a p$-$control chart for the process considering the information in part c and three Sigma control limits$.$ Is the process in control?