Problem $7-11($Algo$)$

How many observations should a time study analyst plan for in an operation that has a standard deviation of $2\mathrm{.}7$ minutes per piece? The goal is to estimate the mean time per piece to within $1\mathrm{.}1$ minutes, with a confidence of $95\mathrm{.}5$ percent. $($Do not round intermediate calculations. Round up your final answer to the next whole number.$)$