A process is in statistical control which x$=199$ and R$=3\mathrm{.}5.$ The control chart uses a sample size of n $=4.$ Specifications are at $200+8.$ The quality characteristic is normally distributed.

Estimate the potential capability of the process.

Estimate the actual process capability.

How much improvement could be made in process performance if the mean could be centered at the nominal value $?$

The advertised weight of frozen food packages is $16($oz$)$ and the specification are $16+0\mathrm{.}3$ oz$.$ Random samples are of size $8$ are selected from the output and weighted. The sample mean and standard deviation are calculated. Information on $25$ such samples yields the following.

$\_($i$=1)^25$xi $=398$ and $\_($i$=1)^25$Si $=3\mathrm{.}00$

Determine the centre lines and control limits for the X $$ and s$-$ charts.

Explain the process mean and standard deviation, assuming that the process is in control.