In a mechanical assembly operation, the first work unit required $7\mathrm{.}83$ min to complete and the learning rate for mechanical assembly is $84\%$ in the Crawford model. Using this learn$-$ ing curve model, determine the unit times to produce $($a$)$ the second unit, $($b$)$ the $10$th unit, and $($c$)$ the $100$th unit. $($d$)$ What are the total cumulative time and the average cumulative time for the $100$ units?