$($x$-$bar chart$)$ A quality control manager at a manufacturing facility has taken four samples

$($each column is a sample$)$ with four observations each of the diameter of a part. Calculate

the center line, upper control limit$,$ and lower control limit for an $x-$bar control chart.

$($Forecasting$)$ The following data are monthly sales of jeans at a local department store. The

buyer would like to forecast sales of jeans for the next month, July.

a$)$ Forecast sales of jeans from March to July using the two$-$period moving average $($i$.$e$.,n=2),$

and forecast sales of jeans from February to July using the exponential smoothing with an

$=0\mathrm{.}2.$

b$)$ Compare the results in a$)$ in terms of accuracy measure$($s$).$ Which forecasting method

would you choose? why?