Fill in the multiple blanks.

a$)$ A quality$-$control technician has been monitoring the output of a milling machine. Each day, the technician selects a random sample of $20$ parts to measure and plot on the control chart. Over $10$ days, the average diameter was $1\mathrm{.}441$ millimeters with a standard deviation of $0\mathrm{.}0675$ millimeters. What is the lower control limit $($LCL$)$ for an X$-$bar chart of this data? Carry four decimal places.

Answer:

millimeters

b$)$ A grinding process has an upper specification of $1\mathrm{.}508$ inches and a lower specification of $1\mathrm{.}407$ inches. A sample of parts had a mean of $1\mathrm{.}45$ inches with a standard deviaiton of $0\mathrm{.}024$ inches. What is the process capability index for this system? Carry four decimal places.

Answer: