The snapback timing method is direct time study was used to obtain the times for

a worker$-$machine task. The recorded times are listed in the table below. Element c is a machine$-$controlled element and the time is constant. Element a$,$ b$,$ and d $,$e$,$f are operator$-$controlled and were performance rated $90\%.$ Element a and b are external to machine$-$controlled element c$.$ Element d $,$e$,$f is internal to the machine element. The machine allowance is zero, and the PFD allowance is $13\%.$ Determine $($a$)$ the normal time and $($b$)$ the standard time for the cycle. The workers actual time spent working during an $8-$hour shift was $7\mathrm{.}08$ hours, and he produced $420$ units of output during this time. Determine $($c$)$ the worker's performance during

the operator$-$controlled portions of the cycle and $($d$)$ the worker's efficiency

during this shift