You want to determine the true mean strength of a new concrete mix with a precision of 50 psi at a confidence level of 99%. If you assume the population standard deviation is 100 psi, what size sample should you use?
Well the standard deviation of a sample mean is the population standard deviation divided by the square root of the sample size.
In other words, if is the population mean of some random variable , and suppose you are going to take samples of size . The sample mean, is another random variable. (It's mean is the population mean, but that is not relevant here).
where is the standard deviation of .
You know 2 of the 2 variables in that equation so have at it!