Determining the Minimum Sample Size Required: Videos & Practice Problems

A manufacturing study finds the standard deviation of part lengths to be $s=0.75\text{ mm}$. The required sample size to estimate the mean length within $0.05\text{ mm}$ with $99\%$ confidence is reported as $n=50$. If the engineer now desires to increase the precision of the estimate to four times its original value while keeping the $99\%$ confidence level, what will be the effect on the required sample size?