If the manager of a bottled water distributor wants to estimate, with \( 95 \% \) confidence, the mean amount of water in a 1-gallon bottle to within \( \pm 0.005 \) gallon and also assumes that the standard deviation is 0.01 gallon, what sample size is needed?
Let \( \mathrm{Z}_{0.025}=1.96 \) and \( \mathrm{Z}_{0.05}=1.64 \).