Question $1(10\%)$ :

The following data were obtained by observing three elements of a financial manager's task.

$\backslash$table$[[,\backslash$table$[[$Observations$],[($second per cycle$)]]],[$Element$,$Performance Rating,$1,2,3,4,5,],[$A$,90\%,33,35,34,32,33,],[$B$,110\%,41,42,40,43,41,],[$C$,85\%,39,41,40,42,41,]]$

a$.$ Using the data and an allowance of $10$ percent of task time, determine a standard tie for the task.

b$.$ Determine the number of observations that would be required to estimate the mean time for element A within $4$ percent of the true value with a confidence of $98$ percent.

c$.$ How many observations would be needed to estimate the mean time for Element C to within $0\mathrm{.}01$ minutes of its actual value with a confidence of $90$ percent?