In my class we learned the formula for finding the sample size $n$ needed to estimate the population mean $\mu$ within a bound $b$ with a level of confidence of $100(1 - \alpha )$% to be $$n = \left(\frac{z_{\alpha / 2} * \sigma}{b}\right)^2$$
This formula works provided we are given the population variance or standard deviation. How would one figure this sort of problem out if $\sigma$ is unknown? Or is there another formula to use in this situation?