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The population standard deviation for the weights of boxes of breakfast cereal is $0$.$6$ ounces. If we want to be $90 \%$ confident that the sample mean is within $1$ ounce of the true population mean, what is the minimum sample size that can be taken?$\newline$\begin{tabular}{|c|c|c|c|c|}$\newline$\hline $\mathbf{z}_{\mathbf{0 . 1 0}}$ & $\mathbf{z}_{\mathbf{0 . 0 5}}$ & $\mathbf{z}_{\mathbf{0 . 0 2 5}}$ & $\mathbf{z}_{\mathbf{0 . 0 1}}$ & $\mathbf{z}_{\mathbf{0 . 0 0 5}}$ \\$\newline$\hline $1$.$282$ & $1$.$645$ & $1$.$960$ & $2$.$326$ & $2$.$576$ \\$\newline$\hline$\newline$\end{tabular}$\newline$Use the table above for the $z$-score, and be sure to round up to the next integer.$\newline$Provide your answer below: