Blackburn Engineering, a parts reseller in Nashville, is currently considering using one of three suppliers. For a specific part, Blackburn$$s upper specification limit $($USL$)$ is $9\mathrm{.}8$ centimeters $($cm$)$ and its lower specification limit $($LSL$)$ is $6\mathrm{.}5$ centimeters $($cm$).$

a$)$ The first supplier, ABC, can adjust its mean but cannot reduce its standard deviation. Its standard deviation is $0\mathrm{.}3$ cm$.$ What is the range $($lower and upper limits$)$ for the mean of the process if ABC wants its process capability index $($Cpk$)$ to satisfy at least Blackburn$$s minimum acceptable value of $1\mathrm{.}33?$