A hotel periodically analyzes its service times to check for variation in service processes. To do this, it uses $R-$charts. Seven

samples, each containing observed checkout time with four different guests, were collected. The average mean and the

average range of the service times are found to be $9\mathrm{.}003$ and $0\mathrm{.}625,$ respectively. If $D_4$ for the $R-$chart is $2\mathrm{.}282,$ the upper

control limit $(UC{L}_R)$ for the $R-$chart will be:

a$.$ greater than $2\mathrm{.}0$ but less than or equal to $2\mathrm{.}5.$

b$.$ less than or equal to $1\mathrm{.}0.$

c$.$ greater than $1\mathrm{.}0$ but less than or equal to $1\mathrm{.}5.$

d$.$ greater than $1\mathrm{.}5$ but less than or equal to $2\mathrm{.}0.$