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How many observations should a stopwatch time$-$study analyst plan for in a task that has a standard deviation of $1\mathrm{.}28$ minutes per piece if the goal is to estimate the mean time per piece to within $0\mathrm{.}5$ minute with a confidence of $90\mathrm{.}0$ percent? $($Round the intermediate calculations to $2$ decimal places. Round the final answer to the next whole number.$)$

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