Problem $2\mathrm{.}6$

A worker performs a repetitive assembly task at a workbench to assemble products. Each product consists of $25$ components. Various hand tools are used in the task. The standard time for the work cycle is $7\mathrm{.}45$min, based on using a PFD allowance factor of $15\%.$ If the worker completes $75$ product units during an $8-$hour shift, determine $($a$)$ the number of standard hours accomplished and $($b$)$ worker efficiency. $($c$)$ If the worker took only one rest break, lasting $13$min, and experienced no other interruptions during the $8$ hours of shift time, determine her worker performance.