The snapback timing method was used to obtain the average times and performance ratings for work elements in a manual repetitive task. See table below. All elements are worker$-$controlled. All elements were performance rated at $80\%.$ Element e is an irregular element performed every five cycles. A $15\%$ allowance for personal time, fatigue, and delays is applied to the cycle. Determine $($a$)$ the normal time and $($b$)$ the standard time for this cycle. If the worker$$s performance during actual production is $120\%$ on all manual elements for seven actual hours worked on an eight$-$hour shift, $($c$)$ how many units will be produced and $($d$)$ what is the worker$$s efficiency?

Work element a$-$ b$-$ c$-$ d$-$ e

Observed time $($min$)0\mathrm{.}32-0\mathrm{.}85-0\mathrm{.}48-0\mathrm{.}55-1\mathrm{.}50$