Problem

Determine $\mu_{\mathrm{x}}^{-}$and $\sigma_{\bar{x}}^{-}$from the given parameters of the population and sample size. \[ \mu=66, \sigma=6, n=25 \] \[ \mu_{\mathrm{x}}=\square \]

Solution

Step 1 :Given the parameters of the population and sample size as follows: \(\mu=66\), \(\sigma=6\), \(n=25\)

Step 2 :Determine \(\mu_{\mathrm{x}}\) and \(\sigma_{\bar{x}}\)

Step 3 :Since \(\mu_{\mathrm{x}}\) is the mean of the population, it is equal to \(\mu\), hence \(\mu_{\mathrm{x}} = 66\)

Step 4 :\(\sigma_{\bar{x}}\) is the standard deviation of the sample mean, which is calculated as \(\sigma / \sqrt{n}\)

Step 5 :Substitute the given values into the formula to get \(\sigma_{\bar{x}} = 6 / \sqrt{25} = 1.2\)

Step 6 :Final Answer: \(\mu_{\mathrm{x}}=\boxed{66}\) and \(\sigma_{\bar{x}}=\boxed{1.2}\)

From Solvely APP
Source: https://solvelyapp.com/problems/HHf27Tc6Zs/

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