Jake's Jumbo Jacks has collected the following information to develop a standard time for building jumbo jacks.

$\backslash$table$[[,$Element $($in minutes$)],[$Observations$,1,2,3,4,5,],[$Cycle $1,2\mathrm{.}18,1\mathrm{.}25,1\mathrm{.}70,2\mathrm{.}74,1\mathrm{.}57,],[$Cycle $2,2\mathrm{.}22,1\mathrm{.}23,1\mathrm{.}75,2\mathrm{.}66,1\mathrm{.}55,],[$Cycle $3,2\mathrm{.}20,1\mathrm{.}29,1\mathrm{.}72,2\mathrm{.}60,1\mathrm{.}57,],[$Cycle $4,2\mathrm{.}18,1\mathrm{.}30,1\mathrm{.}80,2\mathrm{.}56,1\mathrm{.}57,],[$Cycle $5,2\mathrm{.}21,1\mathrm{.}26,1\mathrm{.}84,2\mathrm{.}58,1\mathrm{.}59,],[$Cycle $6,2\mathrm{.}22,1\mathrm{.}22,1\mathrm{.}79,2\mathrm{.}58,1\mathrm{.}61,],[$Cycle $7,2\mathrm{.}17,1\mathrm{.}26,1\mathrm{.}78,2\mathrm{.}60,1\mathrm{.}57,],[$Cycle $8,2\mathrm{.}21,1\mathrm{.}26,1\mathrm{.}75,2\mathrm{.}58,1\mathrm{.}61,],[$Cycle $9,2\mathrm{.}18,1\mathrm{.}30,1\mathrm{.}80,2\mathrm{.}60,1\mathrm{.}55,],[$Cycle $10,2\mathrm{.}17,1\mathrm{.}28,1\mathrm{.}78,2\mathrm{.}58,1\mathrm{.}57,],[$Rating factor,$0\mathrm{.}90,0\mathrm{.}80,1\mathrm{.}10,1\mathrm{.}05,0\mathrm{.}95,],[$Frequency$,1,1,1,1,1,]]$

$($a$)$ Calculate the mean observed time for each element.

$($b$)$ Calculate the normal time for each element.

$($c$)$ Using an allowance factor of $20$ percent of job time, calculate the standard time for each element and for the entire job.

$($d$)$ How many units should be completed each hour if the worker performs at $100$ percent of the standard?

$($e$)$ How many units should be completed each hour if the worker performs at $90$ percent of the standard?