The operations manager at a large widget factory is complaining that since the company has changed to a cheaper supplier for one of the raw materials used for widgets, the quality of their widget has changed. In fact, he has one of the final widgets that has a strength testing below the spec. A new operations employee had previously taken $5$ samples each week over a $10-$week period, and logged the data in the chart below.

Sample data:

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Mean

$27\mathrm{.}4$

$28\mathrm{.}6$

$28\mathrm{.}4$

$27\mathrm{.}8$

$29\mathrm{.}3$

$28\mathrm{.}0$

$27\mathrm{.}2$

$28\mathrm{.}5$

$28\mathrm{.}0$

$27\mathrm{.}5$

Range

$1\mathrm{.}5$

$1\mathrm{.}9$

$0\mathrm{.}9$

$2\mathrm{.}0$

$1\mathrm{.}6$

$1\mathrm{.}6$

$2\mathrm{.}0$

$1\mathrm{.}9$

$2\mathrm{.}1$

$1\mathrm{.}9$

Calculate upper and lower control limits for an Xbar chart using this data