Sheer industries is considering a new computer$-$assisted program to train maintenance employees to do machine repairs. In order to fully evaluate the program, the director of manufacturing requested an estimate of the population mean time required for maintenance employees to complete the computer assisted training. Use $7\mathrm{.}84$ days as a planning value for the population standard deviation. $($Round your answers up to the nearest whole number.$)($a$)$ Assuming $95\%$ confidence, what sample size would be required to obtain a margin of error of $0\mathrm{.}5$ days?$($b$)$ If the precision statement was made with $90\%$ confidence, what sample size would be required to obtain a margin of error of $2$ days?$$