chocolate factory has weighed $4$ chocolate truffles coming out of production over $5$ working

days to obtain the following data, weights are in grams.

Mon Tue Wed Thu Fri

$10$am $30\mathrm{.}5030\mathrm{.}3030\mathrm{.}1530\mathrm{.}6030\mathrm{.}15$

$11$am $29\mathrm{.}7531\mathrm{.}0029\mathrm{.}5032\mathrm{.}0030\mathrm{.}25$

$2$pm $29\mathrm{.}9030\mathrm{.}2029\mathrm{.}7531\mathrm{.}0030\mathrm{.}50$

$3$pm $30\mathrm{.}2530\mathrm{.}5030\mathrm{.}0030\mathrm{.}0029\mathrm{.}70$

a$)$ Group the data by day into five samples and find the sample average and range for each

sample.

Mon Tue Wed Thu Fri

$10$am $30\mathrm{.}5030\mathrm{.}3030\mathrm{.}1530\mathrm{.}6030\mathrm{.}15$

$11$am $29\mathrm{.}7531\mathrm{.}0029\mathrm{.}5032\mathrm{.}0030\mathrm{.}25$

$2$pm $29\mathrm{.}9030\mathrm{.}2029\mathrm{.}7531\mathrm{.}0030\mathrm{.}50$

$3$pm $30\mathrm{.}2530\mathrm{.}5030\mathrm{.}0030\mathrm{.}0029\mathrm{.}70$

x

R

b$)$ Suppose the process has a mean of $30$ and a standard deviation of $0\mathrm{.}3.$ Construct the $3-$sigma

control limits of the mean chart. Is the process in control?