Question content area

Part $1$

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

$300300$

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

$$

Sample No$.$

No$.$ Defectives

Sample No$.$

No$.$ Defectives

Sample No$.$

No$.$ Defectives

$1$

$66$

$11$

$55$

$21$

$1717$

$2$

$44$

$12$

$66$

$22$

$1111$

$3$

$1818$

$13$

$1616$

$23$

$77$

$4$

$1010$

$14$

$55$

$24$

$66$

$5$

$1212$

$15$

$1111$

$25$

$1414$

$6$

$99$

$16$

$77$

$26$

$1111$

$7$

$1313$

$17$

$1313$

$27$

$1515$

$8$

$1010$

$18$

$55$

$28$

$77$

$9$

$66$

$19$

$1717$

$29$

$1313$

$10$

$1414$

$20$

$1515$

$30$

$44$

Part $2$

$$a$)$ Establish

$3$sigma

upper and lower control limits$.$

UCL Subscript pUCLp

$=$

$.065\mathrm{.}065$

$($enter your response as a number between $0$ and$1,$ rounded to three decimal$$ places$).$

Part $3$

LCL Subscript pLCLp

$=$

$.003\mathrm{.}003$

$($enter your response as a number between $0$ and$1,$ rounded to three decimal$$ places$).$

Part $4$

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

A$.$

Since the upper control limit cannot be a negative number.

B$.$

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

C$.$

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

Your answer is correct.

D$.$

Since the upper control limit is positive.

Part $5$

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

The industry standard is

not as strict as

the standard at Birmingham Bank.