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 $350$ records typed by these operators has been noted, as follows:

$\backslash$table$[[\backslash$table$[[$Sample$],[$No$.]],\backslash$table$[[$No$.],[$Defectives$]],\backslash$table$[[$Sample$],[$No$.]],\backslash$table$[[$No$.],[$Defectives$]],\backslash$table$[[$Sample$],[$No$.]],\backslash$table$[[$No$.],[$Defectives$]]],[1,6,11,6,21,17],[2,6,12,4,22,11],[3,19,13,16,23,6],[4,9,14,4,24,7],[5,11,15,10,25,13],[6,8,16,7,26,10],[7,13,17,11,27,14],[8,10,18,4,28,7],[9,5,19,17,29,11],[10,12,20,15,30,4]]$

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

$UC{L}_p=($enter your response as a number between $0$ and $1,$ rounded to three decimal places$).$

$LC{L}_p=($enter your response as a number between $0$ and $1,$ rounded to three decimal places$).$

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

A$.$ Since the upper control limit is positive.

B$.$ Since the upper control limit cannot be a negative number.

C$.$ Since the percent of defective records cannot be a negative number.

D$.$ Since the percent of defective records is always a positive number.

c$)$ The industry standard for the upper control limit is $0\mathrm{.}10.$ What does this imply about Birmingham Bank's own standards?

The industry standard is $$ the standard at Birmingham Bank.

the same as not as strict as stricter than

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