Question $1(10\%)$:

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

Observations

$($second per cycle$)$

Element Performance Rating $12345$

A $90\%3335343233$

B $110\%4142404341$

C $85\%3941404241$

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?