Sample$1$ Sample$2$ Sample $3$ Sample$4$ Sample$5$

$\backslash$table$[[10\mathrm{.}2,10\mathrm{.}3,9\mathrm{.}7,9\mathrm{.}9,9\mathrm{.}8],[9\mathrm{.}9,9\mathrm{.}8,9\mathrm{.}9,10\mathrm{.}3,10\mathrm{.}2],[9\mathrm{.}8,9\mathrm{.}9,9\mathrm{.}9,10\mathrm{.}1,10\mathrm{.}3],[10\mathrm{.}1,10\mathrm{.}4,10\mathrm{.}1,10\mathrm{.}5,9\mathrm{.}7]]$

TABLE$-$I

$\backslash$table$[[$n$,$A $2,$D $3,$D $4],[2,1\mathrm{.}88,0,3\mathrm{.}27],[3,1\mathrm{.}02,0,2\mathrm{.}57],[4,0\mathrm{.}73,0,2\mathrm{.}28],[5,0\mathrm{.}58,0,2\mathrm{.}11],[6,0\mathrm{.}48,0,2\mathrm{.}00],[7,0\mathrm{.}42,0\mathrm{.}08,1\mathrm{.}92],[8,0\mathrm{.}37,0\mathrm{.}14,1\mathrm{.}86],[9,0\mathrm{.}34,0\mathrm{.}18,1\mathrm{.}82],[10,0\mathrm{.}31,0\mathrm{.}22,1\mathrm{.}78],[11,0\mathrm{.}29,0\mathrm{.}26,1\mathrm{.}74]]$

Question $5(4$ points$)$:

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

$\backslash$table$[[1,4],[2,2],[3,5],[4,9]]$

b$.$ Estimate the proportion of defectives $($mean defectives$)$ and standard deviation of the sampling distribution $()$ 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?