The accounts receivable department at Rick Wing Manufacturing has been having difficulty getting customers to pay the full amount of their bills. Many customers complain that the bills are not correct and do not reflect the materials that arrived at their receiving docks. The department has decided to implement SPC in its billing process. To set up control charts, $10$ samples of $50$ bills each were taken over a month's time and the items on the bills checked against the bill of lading sent by the company's shipping department to determine the number of bills that were not correct. The results were:

$\backslash$table$[[$Sample No$.,1,2,3,4,5,6,7,8,9,10],[$No$.$ of Incorrect Bills,$4,3,17,2,1,4,5,2,7,2]]$

a$)$ The value of mean fraction defective $(\frac{?}{\text{b}\text{a}\text{r}}(p))=0\mathrm{.}0940($enter your response as a fraction between $0$ and $1,$ rounded to four decimal places$).$

The control limits to include $99\mathrm{.}73\%$ of the random variation in the billing process are:

$UC{L}_p=($enter your response as a fraction between $0$ and $1,$ rounded to four decimal places$).$