$.($a$)$ The following data were obtained by observing a three$-$step job of a Financial

Manager$$s Assistant.

$($i$)$ Using the data and an allowance of $10\%$ of job time, determine a standard time for

the operation.

$($ii$)$ Determine the number of operations that would be required to estimate the mean time

for element A within $4\%$ of the true value with a confidence level of $98\%.$

Observations $($minutes per cycle$)$

Element Performance Rating $12345$

A $90\%1\mathrm{.}401\mathrm{.}421\mathrm{.}391\mathrm{.}381\mathrm{.}41$

B $120\%2\mathrm{.}102\mathrm{.}052\mathrm{.}001\mathrm{.}851\mathrm{.}80$

C $110\%1\mathrm{.}601\mathrm{.}401\mathrm{.}501\mathrm{.}451\mathrm{.}55$