A work sampling study is to be performed on the art department in apublishing company. The department consists of $22$ artists who work atcomputer graphics workstations developing line drawings based onauthors rough sketches. The duration of the study is $15$ days, seven hoursper day. Line drawings are the main activity performed by the artists, butnot the only activity. The supervisor of the department estimates that theproportion of time spent making line drawings is $75\%$ of each artists day.$($a$)$ At the $95\%$ confidence level, how many observations are required if thelower and upper confidence limits are $0\mathrm{.}72$ and $0\mathrm{.}78,$ respectively. $($b$)$Regardless of your answer in preceding part $($a$),$ a total of $1000$observations were actually taken, and artists were making line drawings in$680$ of those observations. Construct a $97\mathrm{.}5\%$ confidence interval for thetrue proportion of time making line drawings. $($c$)$ Records for the period ofthe study indicate that $5,240$ line drawings were completed. Estimate theaverage time per line drawing? $($d$)$ Determine the standard time for oneline drawing, given that the average performance rating for the artists wasobserved to be $90\%,$ and the allowance for personal time, fatigue, anddelays is $15\%.$