$$ S$6\mathrm{.}18$ 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:

SAMPLE

NO$.$

NO$.$

DEFECTIVE

SAMPLE

NO$.$

NO$.$

DEFECTIVE

SAMPLE

NO$.$

NO$.$

DEFECTIVE

$1711182117$

$251252212$

$3191316236$

$410144247$

$51115112513$

$681682610$

$71217122714$

$89184286$

$961962912$

$10132016303$

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

b$)$ Why can the lower control limit not be a negative number?

c$)$ The industry standards for the upper and lower control limits

are $0\mathrm{.}10$ and $0\mathrm{.}01,$ respectively. What does this imply about

Birmingham Bank$$s own standards? PX