$1)$ Five data entry operators work at the data processing department of the Royal 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

$1$

$18$

$11$

$17$

$21$

$7$

$2$

$5$

$12$

$12$

$22$

$5$

$3$

$16$

$13$

$6$

$23$

$19$

$4$

$4$

$14$

$7$

$24$

$10$

$5$

$11$

$15$

$13$

$25$

$11$

$6$

$8$

$16$

$10$

$26$

$8$

$7$

$12$

$17$

$4$

$27$

$12$

$8$

$4$

$18$

$6$

$28$

$9$

$9$

$6$

$19$

$12$

$29$

$6$

$10$

$16$

$20$

$3$

$30$

$13$

$$

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

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

$$ The industry standards for the upper and lower control limits are $0\mathrm{.}11$ and $0\mathrm{.}02,$ respectively. What does this imply about Royal Bank$$s own standards?

$$

$$