How many observations should a time study analyst plan for in an operation that has a standard deviation of $1\mathrm{.}1$ minutes per plece? The goal is to estimate the mean time per plece to within $0\mathrm{.}4$ minutes, with a confidence of $95\mathrm{.}5$ percent.

Note: Do not round Intermediate calculations. Round up your final answer to the next whole number.

Number of observations