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 $200$ records typed by these

operators has been$$noted$,$ as$$follows:

$$Sample No$.$No$.$ DefectivesSample No$.$No$.$ DefectivesSample No$.$No$.$ Defectives$181162116241242211318131523741014424751115122513671682611712171227138818428797191829131014201530$a$)$ Establish $3\backslash$sigma upper and lower control limits$.$UCLp $=($enter$$your response as a

number between $0$

and$1,$rounded to three

decimal$$places$).$LCPp $=($enter$$your response as a number between

$0$ and$1,$rounded to three

decimal$$places$).$b$)$ Why can the lower limit not be a negative number? $($I actually

know this one but I wanna get all the points down$)$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? 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 $300$ 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$]]],[1,6,11,6,21,16],[2,4,12,6,22,11],[3,20,13,16,23,5],[4$

$,9,14,4,24,8],[5,12,15,11,25,13],[6,7,16,7,26,10],[7,12,17,11,27,13],[8,10,18,5,28,7],[9,7,19,18,29,13],[10,12,20,16,30,2]]$