Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 190.4 ft and standard deviation 90.3 ft. You intend to measure a random sample of n = trees. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal 209

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**Understanding the Distribution of Tree Heights**

Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with a mean of 190.4 ft and a standard deviation of 90.3 ft.

To estimate this, you will measure a random sample of size \( n = 209 \) trees. The bell curve shown below represents the distribution of these sample means. The horizontal axis is scaled by the standard error of the sampling distribution. Complete the indicated boxes with values rounded to two decimal places.

**Graph Explanation**

The graph is a normal distribution curve (bell curve) illustrating the distribution of sample means for the height of the trees. Two boxes next to the graph are labeled for mean (\( \mu_{\bar{x}} \)) and standard error (\( \sigma_{\bar{x}} \)) of the sample means:

- \( \mu_{\bar{x}} \): Represents the mean of the sample means.
- \( \sigma_{\bar{x}} \): Represents the standard error of the sample means, which can be calculated using the formula:
  \[
  \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
  \]

Where \( \sigma \) is the standard deviation of the population (90.3 ft) and \( n \) is the sample size (209).

This activity will aid in understanding the application of sampling distributions and their characteristics.

**Action Required**

- Calculate and enter the mean (\( \mu_{\bar{x}} \)) and standard error (\( \sigma_{\bar{x}} \)) to two decimal places in the provided spaces.

**Options**

- For help, select "Message instructor."
- To submit your response, click "Submit Question."
Transcribed Image Text:**Understanding the Distribution of Tree Heights** Let \( X \) represent the full height of a certain species of tree. Assume that \( X \) has a normal probability distribution with a mean of 190.4 ft and a standard deviation of 90.3 ft. To estimate this, you will measure a random sample of size \( n = 209 \) trees. The bell curve shown below represents the distribution of these sample means. The horizontal axis is scaled by the standard error of the sampling distribution. Complete the indicated boxes with values rounded to two decimal places. **Graph Explanation** The graph is a normal distribution curve (bell curve) illustrating the distribution of sample means for the height of the trees. Two boxes next to the graph are labeled for mean (\( \mu_{\bar{x}} \)) and standard error (\( \sigma_{\bar{x}} \)) of the sample means: - \( \mu_{\bar{x}} \): Represents the mean of the sample means. - \( \sigma_{\bar{x}} \): Represents the standard error of the sample means, which can be calculated using the formula: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] Where \( \sigma \) is the standard deviation of the population (90.3 ft) and \( n \) is the sample size (209). This activity will aid in understanding the application of sampling distributions and their characteristics. **Action Required** - Calculate and enter the mean (\( \mu_{\bar{x}} \)) and standard error (\( \sigma_{\bar{x}} \)) to two decimal places in the provided spaces. **Options** - For help, select "Message instructor." - To submit your response, click "Submit Question."
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