Compute the following equation; $\sigma_{x}=15$ $N=36$ $\bar{X}=105$ \[ \begin{array}{c} \sigma_{\bar{X}}=\frac{\sigma_{X}}{\sqrt{N}}= \\ z_{\text {obt }}=\frac{\bar{X}-\mu}{\sigma_{\bar{X}}}= \end{array} \] What is \[ \sigma_{\bar{X}}= \]

Step 1 ：Given that the standard deviation of the population, denoted as \(\sigma_{X}\), is 15 and the size of the sample, denoted as \(N\), is 36.

Step 2 ：We can calculate the standard deviation of the mean, denoted as \(\sigma_{\bar{X}}\), using the formula \(\sigma_{\bar{X}}=\frac{\sigma_{X}}{\sqrt{N}}\).

Step 3 ：Substituting the given values into the formula, we get \(\sigma_{\bar{X}}=\frac{15}{\sqrt{36}}\).

Step 4 ：Solving the equation, we find that \(\sigma_{\bar{X}}=2.5\).

Step 5 ：Final Answer: The standard deviation of the mean, \(\sigma_{\bar{X}}\), is \(\boxed{2.5}\).