Q$1.$

The time to make beds at a motel should fall into an agreed$-$on range of times. A sample of four maids was selected, and the time needed to make a bed was observed on three different occasions:

Service Time, Sec. Maid Sample $1$ Sample $2$ Sample $3$ Ann $12090150$ Linda $130110140$ Marie $200180175$ Michael $165155140$

a$.$ Determine the upper and lower control limits for an bar$($X$)-$chart and an R$-$chart with a sample size of four.

b$.$ After the control chart was established, a sample of four observations had the following times in seconds: $185,150,192,$ and $178.$ Is corrective action needed?

Change the values for Ann to $120+20$f$,90-20$f$,150+20$f in sample $1,2$ and $3,$ respectively before you answer. And use f$=0\mathrm{.}4$