We need to establish the $3$ sigma control limits for a production or manufacturing line. We collect

n $=5$ items at periodic intervals during a production shift. The mean and variance are found to be

normally distributed. After $40$ subgroups have been analyzed, we have

a$)$Compute the three sigma control limit for the mean and variance.

$($b$)$ If the customer$$s specification limits are $40\backslash$pm $2\mathrm{.}0,$ what are your conclusions regarding the ability of

your production process to produce items conforming to specifications?