The data in the following table represent time$-$study observations for a woodworking operation$/$task$.$Observations $($minutes per cycle$)2$Element$123$Performance Rating$1101\mathrm{.}200\mathrm{.}830\mathrm{.}58$minutesb. How many observations would be needed to estimate the mean time for element $1$ within $1$ percent of its true value with a $95\mathrm{.}5$ percent confidence? $($Round the final answer to the next whole number.$)$Observationsc$.$ How many observations would be needed to estimate the mean time for element $1$ within $0\mathrm{.}01$ minute of its true value with a $95\mathrm{.}5$ percent confidence? $($Round the final answer to the next whole number.$)$Observations$11510510\mathrm{.}5330\mathrm{.}871\mathrm{.}171\mathrm{.}161\mathrm{.}221\mathrm{.}241\mathrm{.}151\mathrm{.}328\mathrm{.}54$"Unusual delay, disregard time$\mathrm{.}60\mathrm{.}600\mathrm{.}850\mathrm{.}820\mathrm{.}5950\mathrm{.}5240\mathrm{.}78$a$.$ Based on the observations, determine the standard time for the operation, assuming an allowance of $20$ percent of task times. $($Round the final answer to $3$ decimal places.$)$Standard time