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How many work cycles should be timed to estimate the average cycle time to within $2$ percent of the sample mean with a confic of $99\mathrm{.}0$ percent if a pilot study yielded these times $($in minutes$)$: $3\mathrm{.}5,3\mathrm{.}2,3\mathrm{.}8,3\mathrm{.}5,3\mathrm{.}1,$ and $3\mathrm{.}8?($Round the final answer to the ne whole number.$)$

Work cycles