$(4$ points$)$ A time study was conducted on a job that contains four elements. The observed times and performance ratings for six cycles are shown in the following table.

$\backslash$table$[[,$Observations $($minutes per cycle$)],[$Element$,$Rating,$1,2,3,4,5,6,],[1,90,0\mathrm{.}41,0\mathrm{.}46,0\mathrm{.}36,0\mathrm{.}36,0\mathrm{.}36,0\mathrm{.}36,],[2,85,1\mathrm{.}41,1\mathrm{.}41,1\mathrm{.}36,1\mathrm{.}36,1\mathrm{.}36,1\mathrm{.}41,],[3,100,0\mathrm{.}76,0\mathrm{.}76,0\mathrm{.}66,0\mathrm{.}71,0\mathrm{.}76,0\mathrm{.}71,],[4,85,1\mathrm{.}01,1\mathrm{.}06,1\mathrm{.}01,1\mathrm{.}06,1\mathrm{.}06,1\mathrm{.}11,]]$

a$.$ Determine the average cycle time for each element.

b$.$ Find the normal time for each element.

c$.$ Assuming an allowance factor of $11$ percent of job time, compute the standard time for this job.