Five data entry operators work of Data Processing department each day for $20$ working days the number of defective records in a sample of $250$ records typed by these operators has been noted, as follows:

SampleNo. No$.$ Defective SampleNo. No$.$ Defective

$171112$

$25125$

$3101320$

$410144$

$5111511$

$68168$

$761712$

$89184$

$96196$

$10132025$

a$)$ Establish a three$-$sigma control chart for monitoring the number of defective records.

What is the upper limit$?$

What is the lower limit$?$

b$)$ Based on the chart created in $($a$),$ was there any day when the process was not in control? Which days?

c$)$ What action or corrective action would you suggest to eliminate the out of control event?