## Sample Size to estimate mean

- STATISTICS

Sample size to estimate mean The minimum sample size required to estimate the population mean $\mu$ is $$ \begin{aligned} n &= \bigg(\frac{z*\sigma}{E}\bigg)^2 \end{aligned} $$
where
$\sigma$ is the population standard deviation $z=z_{\alpha/2}$ is the critical value of $Z$ $E$ is the margin of error. Example 1 An efficiency expert wishes to determine the average time that it takes to drill three holes in a certain metal clamp. How large a sample will she need to be 90% confident that her sample mean will be within 15 seconds of the true mean?