# Math Help - Sample Size

1. ## Sample Size

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?

2. 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 $\sigma$ is the population mean of some random variable $X$, and suppose you are going to take samples of size $N$. The sample mean, $\bar{X}$ is another random variable. (It's mean is the population mean, but that is not relevant here).

$\sigma_{\bar{X}} = \sigma/\sqrt{N}$

where $\sigma_{\bar{X}}$ is the standard deviation of $\bar{X}$.

You know 2 of the 2 variables in that equation so have at it!