Your$$ supervisor, Lisa$$ Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a mean weight of $50$ grams and a range of $3\mathrm{.}5$ grams. The following table contains the data for a sample size of nequals$6$ taken during the past $3$ hours:

$$

Sample

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

x overbar

$55$

$47$

$49$

$50$

$52$

$57$

$55$

$48$

$51$

$56$

R

$3$

$1$

$5$

$3$

$2$

$6$

$3$

$2$

$2$

$3$

Part $2$

Set the control limits for this process for the x overbar$-$chart when the machine is working properly.