MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Question
**Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 550, 640, 500, 480, and 290?**
[Submit Answer] [Details] [Previous Answers]
ASWESBE9 3.E.036
---
#### Explanation for Z-Scores
To find the z-scores for each data value, you use the formula:
\[ Z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the data value,
- \( \mu \) is the mean of the sample (500 in this case),
- \( \sigma \) is the standard deviation (100 in this case).
**Data Values and Calculation of Z-Scores:**
1. **For 550:**
\[ Z = \frac{(550 - 500)}{100} = \frac{50}{100} = 0.5 \]
2. **For 640:**
\[ Z = \frac{(640 - 500)}{100} = \frac{140}{100} = 1.4 \]
3. **For 500:**
\[ Z = \frac{(500 - 500)}{100} = \frac{0}{100} = 0 \]
4. **For 480:**
\[ Z = \frac{(480 - 500)}{100} = \frac{-20}{100} = -0.2 \]
5. **For 290:**
\[ Z = \frac{(290 - 500)}{100} = \frac{-210}{100} = -2.1 \]
By using these calculations, you can determine the z-scores for each listed data value relative to the given sample mean and standard deviation.
---
If there are further questions or concepts you would like to understand better, feel free to use the "Ask Your Teacher" feature or check your "My Notes" section for additional resources.](https://content.bartleby.com/qna-images/question/bac5cd56-9885-4a25-8e51-dfc1bb78a29e/1a383b76-5ee6-45e3-9377-c5e50ef848f2/ozqpbc9_processed.jpeg)
Transcribed Image Text:---
### Question
**Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 550, 640, 500, 480, and 290?**
[Submit Answer] [Details] [Previous Answers]
ASWESBE9 3.E.036
---
#### Explanation for Z-Scores
To find the z-scores for each data value, you use the formula:
\[ Z = \frac{(X - \mu)}{\sigma} \]
where:
- \( X \) is the data value,
- \( \mu \) is the mean of the sample (500 in this case),
- \( \sigma \) is the standard deviation (100 in this case).
**Data Values and Calculation of Z-Scores:**
1. **For 550:**
\[ Z = \frac{(550 - 500)}{100} = \frac{50}{100} = 0.5 \]
2. **For 640:**
\[ Z = \frac{(640 - 500)}{100} = \frac{140}{100} = 1.4 \]
3. **For 500:**
\[ Z = \frac{(500 - 500)}{100} = \frac{0}{100} = 0 \]
4. **For 480:**
\[ Z = \frac{(480 - 500)}{100} = \frac{-20}{100} = -0.2 \]
5. **For 290:**
\[ Z = \frac{(290 - 500)}{100} = \frac{-210}{100} = -2.1 \]
By using these calculations, you can determine the z-scores for each listed data value relative to the given sample mean and standard deviation.
---
If there are further questions or concepts you would like to understand better, feel free to use the "Ask Your Teacher" feature or check your "My Notes" section for additional resources.
![**Interactive Tutorial: Calculating Z-scores**
---
### Z-Scores Calculations
To practice calculating Z-scores for given data points, input your results in the provided fields. Ensure your calculations are accurate and based on the formula for computing Z-scores.
#### What is a Z-Score?
A z-score indicates how many standard deviations a data point is from the mean of the data set. The formula to calculate the z-score is:
\[
z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the data point
- \( \mu \) is the mean of the data set
- \( \sigma \) is the standard deviation of the data set
### Practice Problems:
1. Determine the z-score for the data point 480.
2. Determine the z-score for the data point 290.
#### Input your calculated Z-scores below:
- z-score for 480: [Enter a number] 
- z-score for 290: [Enter a number] 
### Need Help?
If you need assistance with calculating Z-scores, click on the "Read It" button for a detailed explanation and additional examples.
**Read It:**
---
### Additional Features:
- **Show My Work (Optional)**: Use this section to explain your step-by-step process of calculating the Z-scores. Providing detailed workings can help reinforce your understanding and identify any errors in calculations.
#### Show My Work:
### Submit Your Answer:
After entering and reviewing your Z-scores, click on the "Submit Answer" button to check your results.
**Submit Answer**
---](https://content.bartleby.com/qna-images/question/bac5cd56-9885-4a25-8e51-dfc1bb78a29e/1a383b76-5ee6-45e3-9377-c5e50ef848f2/hubkk2d_processed.jpeg)
Transcribed Image Text:**Interactive Tutorial: Calculating Z-scores**
---
### Z-Scores Calculations
To practice calculating Z-scores for given data points, input your results in the provided fields. Ensure your calculations are accurate and based on the formula for computing Z-scores.
#### What is a Z-Score?
A z-score indicates how many standard deviations a data point is from the mean of the data set. The formula to calculate the z-score is:
\[
z = \frac{X - \mu}{\sigma}
\]
where:
- \( X \) is the data point
- \( \mu \) is the mean of the data set
- \( \sigma \) is the standard deviation of the data set
### Practice Problems:
1. Determine the z-score for the data point 480.
2. Determine the z-score for the data point 290.
#### Input your calculated Z-scores below:
- z-score for 480: [Enter a number] 
- z-score for 290: [Enter a number] 
### Need Help?
If you need assistance with calculating Z-scores, click on the "Read It" button for a detailed explanation and additional examples.
**Read It:**
---
### Additional Features:
- **Show My Work (Optional)**: Use this section to explain your step-by-step process of calculating the Z-scores. Providing detailed workings can help reinforce your understanding and identify any errors in calculations.
#### Show My Work:
### Submit Your Answer:
After entering and reviewing your Z-scores, click on the "Submit Answer" button to check your results.
**Submit Answer**
---
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