The Money Pit Mortgage Company is interested in monitoring the performance of the mortgage

process. Fifteen samples of five completed mortgage transactions each were taken during a period

when the process was believed to be in control. The times to complete the transactions were measured.

The means and ranges of the mortgage process transaction times, measured in days, are as follows:

Subsequently, samples of size $5$ were taken from the process every week for the next $10$ weeks. The

times were measured and the following results obtained:

Click the icon to view the table of factors for calculating three$-$sigma limits for the $\stackrel{}{x}-$chart

and R$-$chart.

a$.$ Construct the control charts for the mean and the range, using the original $15$ samples.

Set up the R$-$chart by specifying the center line and three$-$sigma control limits below. $($Enter your

responses rounded to two decimal places.$)$