Questions: Determine (mubarx) and (sigmabarx) from the given parameters of the population and sample size. [ mu=67, sigma=5, n=27 mubarx=square ]

Transcript text: Determine $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$ from the given parameters of the population and sample size. \[ \begin{array}{l} \mu=67, \sigma=5, n=27 \\ \mu_{\bar{x}}=\square \end{array} \]

Solution

Solution Steps

Step 1: Calculate the mean of the sampling distribution of the sample mean

The mean of the sampling distribution of the sample mean ($\mu_{\bar{x}}$) is equal to the population mean ($\mu$). Therefore, $\mu_{\bar{x}} = \mu = 67$.

Step 2: Calculate the standard deviation of the sampling distribution of the sample mean

The standard deviation of the sampling distribution of the sample mean ($\sigma_{\bar{x}}$) is calculated by dividing the population standard deviation ($\sigma$) by the square root of the sample size ($n$). Therefore, $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = 0.96$.

Final Answer:

The mean ($\mu_{\bar{x}}$) of the sampling distribution of the sample mean is 67, and the standard deviation ($\sigma_{\bar{x}}$) of the sampling distribution of the sample mean is 0.96.

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