S$6\mathrm{.}33$ 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

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$6$

taken during the past $3$ hours:

SAMPLE NUMBER $12345678910$

SAMPLE AVERAGE $55474950525755485156$

SAMPLE RANGE $3153263223$

What are the

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$-$chart control limits when the machine is working properly?

What are the R$-$chart control limits when the machine is working properly?

What seems to be happening? $($HINT: Graph the data points. Run charts may be helpful.$)$ PX