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