A dynamometer is used to determine the power transmitted to the wheels of an electric car by simultaneously measuring the torque T and angular rotation rate of the wheels. The power P is determined according to P $=$ T $.$ With the car$$s settings held constant, the following measurements are made: T $($N$$m$)407388408414$ $($rad$/$s$)4757473547774716($a$)(2$ points$)$ Calculate the mean torque T and standard deviation of the torque, ST $.($b$)(2$ points$)$ Determine the random uncertainty of the torque, with $95\%$ confidence. $($c$)(2$ points$)$ Calculate the mean rotation rate and standard deviation of the rotation rate S$.($d$)(2$ points$)$ Determine the random uncertainty of the rotation rate, with $95\%$ confidence. $($e$)(2$ points$)$ Calculate the mean power P and standard deviation of the power SP $.($f$)(2$ points$)$ Determine the random uncertainty of the power, with $95\%$ confidence. $($g$)(6$ points$)$ According to its manufacturer, the dynamometer measures both torque and rotation rate with accuracy $1\%$ of the reading, with $95\%$ confidence. Determine the systematic uncertainty in the power measurement. $($h$)(2$ points$)$ Determine the total uncertainty in the power measurement at $95\%$ confidence. $($i$)(4$ points$)$ To reduce the total uncertainty, what would you do first? $($j$)(5$ points$)$ Which, if any, of the measurements of torque and rotation rate are outliers, according to Thompson$$s test?