Questions: Use the table from part (a) to find μₓ̄ (the mean of the sampling distribution of the sample mean) and σₓ̄ (the standard deviation of the sampling distribution of the sample mean). Write your answers to two decimal places. μₓ̄= σₓ̄=

Use the table from part (a) to find μₓ̄ (the mean of the sampling distribution of the sample mean) and σₓ̄ (the standard deviation of the sampling distribution of the sample mean). Write your answers to two decimal places. μₓ̄= σₓ̄=
Transcript text: Use the table from part (a) to find $\mu_{\bar{x}}$ (the mean of the sampling distribution of the sample mean) and $\sigma_{\overline{-}}$ (the standard deviation of the sampling distribution of the sample mean). Write your answers to two decimal places. \[ \begin{array}{l} \mu_{\bar{x}}= \\ \sigma_{\bar{x}}= \end{array} \]
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Solution

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Solution Steps

To find the mean of the sampling distribution of the sample mean (\(\mu_{\bar{x}}\)), we use the fact that it is equal to the population mean. For the standard deviation of the sampling distribution of the sample mean (\(\sigma_{\bar{x}}\)), we divide the population standard deviation by the square root of the sample size \(n\).

Step 1: Calculate the Mean of the Sampling Distribution

The mean of the sampling distribution of the sample mean, denoted as \( \mu_{\bar{x}} \), is equal to the population mean. Given that the population mean is \( 4.33 \), we have: \[ \mu_{\bar{x}} = 4.33 \]

Step 2: Calculate the Standard Deviation of the Sampling Distribution

The standard deviation of the sampling distribution of the sample mean, denoted as \( \sigma_{\bar{x}} \), is calculated using the formula: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] where \( \sigma \) is the population standard deviation and \( n \) is the sample size. Given that \( \sigma = 0.33 \) and assuming \( n = 1 \), we find: \[ \sigma_{\bar{x}} = \frac{0.33}{\sqrt{1}} = 0.33 \]

Final Answer

Thus, the results are: \[ \mu_{\bar{x}} = 4.33 \] \[ \sigma_{\bar{x}} = 0.33 \] The final boxed answers are: \[ \boxed{\mu_{\bar{x}} = 4.33} \] \[ \boxed{\sigma_{\bar{x}} = 0.33} \]

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