Five data entry operators work at the data processing department of the Birmingham Bank. Each day for $30$ days, the number of defective records in a sample of $250$ records typed by these operators has been noted, as follows:

$\backslash$table$[[$Sample No$.,$No$.$ Defective,Sample No$.,$No$.$ Defective,Sample No$.,$No$.$ Defective$],[1,7,11,18,21,17],[2,5,12,16,22,12],[3,19,13,4,24,6],[4,10,14,11,25,13],[5,11,15,8,26,10],[6,8,16,12,27,14],[8,12,17,4,29,12]]$

Using a p$-$chart

a$.$ Establish $3$ upper and lower control limits

UCL$=0\mathrm{.}077$

$LCL=0\mathrm{.}003$

UCL$=0\mathrm{.}075$

$LCL=0\mathrm{.}003$

UCL$=0\mathrm{.}077$

$LCL=0\mathrm{.}001$

UCL$=0\mathrm{.}077$

$LCL=0\mathrm{.}005$