A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![### Calculating the Sample Mean and Margin of Error
#### Problem Statement
**Use the given confidence interval to find the margin of error and the sample mean.**
**Confidence Interval:** (13.2, 20.2)
---
#### Solution Steps
1. **Sample Mean Calculation:**
- **Formula:** \( \text{Sample Mean} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \)
- Plug in the values from the confidence interval:
\( \frac{13.2 + 20.2}{2} \)
- Simplify to get the sample mean:
\( \frac{33.4}{2} = 16.7 \)
- **Solution:**
- The sample mean is **16.7**.
2. **Margin of Error Calculation:**
- **Formula:** \( \text{Margin of Error} = \text{Upper Limit} - \text{Sample Mean} \)
- Subtract the sample mean from the upper limit:
\( 20.2 - 16.7 = 3.5 \)
- **Solution:**
- The margin of error is **3.5**.
#### User Input Field
- The sample mean is: [16.7] (Type an integer or a decimal.)
---
In this exercise, you learned how to calculate the sample mean and margin of error given a confidence interval. These concepts are essential in statistics for estimating population parameters.](https://content.bartleby.com/qna-images/question/1a5e68af-43fc-4f18-979d-78274e50dd4a/1e941695-d8e7-487c-bba6-4ceccda842a2/4ofj48n_processed.png)
Transcribed Image Text:### Calculating the Sample Mean and Margin of Error
#### Problem Statement
**Use the given confidence interval to find the margin of error and the sample mean.**
**Confidence Interval:** (13.2, 20.2)
---
#### Solution Steps
1. **Sample Mean Calculation:**
- **Formula:** \( \text{Sample Mean} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \)
- Plug in the values from the confidence interval:
\( \frac{13.2 + 20.2}{2} \)
- Simplify to get the sample mean:
\( \frac{33.4}{2} = 16.7 \)
- **Solution:**
- The sample mean is **16.7**.
2. **Margin of Error Calculation:**
- **Formula:** \( \text{Margin of Error} = \text{Upper Limit} - \text{Sample Mean} \)
- Subtract the sample mean from the upper limit:
\( 20.2 - 16.7 = 3.5 \)
- **Solution:**
- The margin of error is **3.5**.
#### User Input Field
- The sample mean is: [16.7] (Type an integer or a decimal.)
---
In this exercise, you learned how to calculate the sample mean and margin of error given a confidence interval. These concepts are essential in statistics for estimating population parameters.
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