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

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?