Problem $2\mathrm{.}1$I

The normal time for a work cycle in a worker$-$machine system is $6\mathrm{.}27$min. For setting the standard time, the PFD allowance factor is $12\%,$ and the machine allowance factor is $25\%.$ The work cycle includes manual elements totaling a normal time of $5\mathrm{.}92$min, all but $0\mathrm{.}65$min of which are performed as internal elements. Determine $($a$)$ the standard time for the cycle and $($b$)$ the daily output at standard performance. $($c$)$ During an $8-$hour shift, the worker lost $39$min due to personal time, rest breaks, and delays, and she produced $72$ pieces. What was the worker's pace on the operator$-$controlled portion of the shift?