Problem $3$: The continuous timing method is used to direct time study a manual task cycle consisting of four elements: $a,b,c,$ and $d.$ Two parts are produced each cycle. Element $d$ is an irregular element performed once every six cycles. All elements were performance rated at $80\%.$ The PDF allowance is $12\%.$ Determine $($a$)$ the normalized time for the cycle, $($b$)$ the standard time per part, $($c$)$ the worker's efficiency if the worker completes $844$ parts in an $8-$hour shift during which she works $7$ hours and $10$ min. $(8$ points$)$

Work element $a,b,c,d$

Observed time $(min),0\mathrm{.}400\mathrm{.}701\mathrm{.}001\mathrm{.}46$