SUPP

$-56\mathrm{.}18$ 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:

$\backslash$table$[[\backslash$table$[[$SAMPLE$],[$NO$.]],\backslash$table$[[$NO$.],[$DEFECTIVE$]],\backslash$table$[[$SAMPLE$],[$NO$.]],\backslash$table$[[$NO$.],[$DEFECTIVE$]],\backslash$table$[[$SAMPLE$],[$NO$.]],\backslash$table$[[$NO$.],[$DEFECTIVE$]]],[1,7,11,18,21,17],[2,5,12,5,22,12],[3,19,13,16,23,6],[4,10,14,4,24,7],[5,11,15,11,25,13],[6,8,16,8,26,10],[7,12,17,12,27,14],[8,9,18,4,28,6],[10,6,19,6,29,12]]$

a$)$ Establish $3$ 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