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?