Data for a Mammography Center procedures are given in the table. The volumes shown are for a $5$month period $($use can use $30$ days per month$).$ The center works only one $8-$hour shift per day $($so the shift volumes and daily volumes are the same$).$ The indirect support hours are $\mathrm{.}13$ hours per procedure and fixed administrative hours required are $4$ per shift. The unit has a target utilization rate of $83\%.$ Sick, vacation, and other leave days total $30$ per year and workers get $2$ days off per week.

$\backslash$table$[[$Mammography Center Procures,$5$ Month Volume,Standard Hours$],[$Procedure $1,218,\mathrm{.}2],[$Procedure $2,191,\mathrm{.}26],[$Procedure $3,100,\mathrm{.}53],[$Procedure $4,19,\mathrm{.}58],[$Procedure $5,134,\mathrm{.}77],[$Procedure $6,1576,\mathrm{.}23],[$Procedure $7,1612,\mathrm{.}31],[$Procedure $8,9345,\mathrm{.}36],[$Procedure $9,121,\mathrm{.}44],[$Procedure $10,345,\mathrm{.}76],[$Procedure $22,213,\mathrm{.}81]]$

a$.$ Compute the average volume for a shift based on the volumes. How many technicians would be needed for an average shift?

b$.$ What is the FTE requirement for radiology technicians?