Hz = 20 Oz = 0.64 v 18.72 X 20 V 2 21.28 X

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Can i get assistance with the 2 points i got incorrectly on the graph please.

### Analysis of Newt Length Distribution

**Introduction:**
The image provided includes an analysis of the full length \(X\) of a certain species of newt. We assume \(X\) follows a normal probability distribution with a mean length of 20 inches and a standard deviation of 7.9 inches.

### Sampling Distribution:
To analyze the distribution of newt lengths further, we consider a random sample of \(n = 151\) newts. The diagram below illustrates the bell curve representing the distribution of these sample means.

#### Bell Curve Description:
- **Horizontal Axis Scale:** This represents the standard error of the sampling distribution.
- **Vertical Axis:** Displays the frequency of sample means.

### Calculation:
For this sample:
- **Mean of sample means (\(\mu_{\overline{X}}\)) = 20 inches**
- **Standard error of the sample means (\(\sigma_{\overline{X}}\)) = 0.64 inches**

#### Graph Inclusion:
Below the bell curve, pivotal points are marked for different values. Each point is as follows:
- 18.72 inches
- 20 inches (mean of sample means)
- 21.28 inches

### Conclusion:
The given problem highlights the process of determining the distribution of sample means for the length of a specific species of newt. This is done by recording the lengths of 151 newts and calculating the mean and standard error, demonstrating their normal distribution characteristics.

> **Note:** Calculations should be precise, rounded to two decimal places, as illustrated in the graph.

This explanation comprises a thorough transcription and elucidation suitable for an educational context, ensuring a comprehensive understanding of the concept of sampling distributions in a biological context.
Transcribed Image Text:### Analysis of Newt Length Distribution **Introduction:** The image provided includes an analysis of the full length \(X\) of a certain species of newt. We assume \(X\) follows a normal probability distribution with a mean length of 20 inches and a standard deviation of 7.9 inches. ### Sampling Distribution: To analyze the distribution of newt lengths further, we consider a random sample of \(n = 151\) newts. The diagram below illustrates the bell curve representing the distribution of these sample means. #### Bell Curve Description: - **Horizontal Axis Scale:** This represents the standard error of the sampling distribution. - **Vertical Axis:** Displays the frequency of sample means. ### Calculation: For this sample: - **Mean of sample means (\(\mu_{\overline{X}}\)) = 20 inches** - **Standard error of the sample means (\(\sigma_{\overline{X}}\)) = 0.64 inches** #### Graph Inclusion: Below the bell curve, pivotal points are marked for different values. Each point is as follows: - 18.72 inches - 20 inches (mean of sample means) - 21.28 inches ### Conclusion: The given problem highlights the process of determining the distribution of sample means for the length of a specific species of newt. This is done by recording the lengths of 151 newts and calculating the mean and standard error, demonstrating their normal distribution characteristics. > **Note:** Calculations should be precise, rounded to two decimal places, as illustrated in the graph. This explanation comprises a thorough transcription and elucidation suitable for an educational context, ensuring a comprehensive understanding of the concept of sampling distributions in a biological context.
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