Ten samples of $15$ parts each were taken from an ongoing process to establish a p$-$chart for control. The samples and the number of defectives in each are shown in the following table:

$\backslash$table$[[$SAMPLE$,n,\backslash$table$[[$NUMBER OF$],[$DEFECTIVE$],[$ITEMS IN THE$],[$SAMPLE$]]],[1,15,1],[2,15,1],[3,15,1],[4,15,0],[5,15,2],[6,15,3],[7,15,1],[8,15,0],[9,15,2],[10,15,1]]$

a$.$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(p),S_p,$UCL, and $LCL$ for a $p-$chart of $95$ percent confidence $(1\mathrm{.}96$ standard deviation$).$

Note: Leave no cells blank. Round up any negative LCL value to $"0".$ Round your answers to $3$ decimal places.