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The question you're asking appears to relate to the statistical distribution of commute times in New Orleans based on a given mean and standard deviation.

### Given information:
- **Mean commute time**: 25.8 minutes
- **Standard deviation**: 6.2 minutes
- The questions involve calculating percentages and intervals within 1, 2, and 2.5 standard deviations from the mean, following a normal distribution.

### To summarize the parts of the question:

1. **Part (a)**: What is the minimum percentage of commuters with commute times within 1 standard deviation of the mean?
2. **Part (b)**: What is the percentage within 2.5 standard deviations?
3. **Part (c)**: What percentage have commute times between 13.4 minutes and 38.2 minutes (this is within 2 standard deviations from the mean)?

### Explanation of how to solve this:

1. **For part (a)**:
   - The empirical rule (68-95-99.7 rule) tells us that:
     - About **68%** of the data lies within 1 standard deviation of the mean in a normal distribution.
   
2. **For part (b)**:
   - Using a z-score table or empirical rule approximation, we find that about **98.8%** of the data lies within 2.5 standard deviations of the mean.
   
3. **For part (c)**:
   - The values 13.4 minutes and 38.2 minutes represent the commute times that fall within 2 standard deviations of the mean. According to the empirical rule, **95%** of the data lies within 2 standard deviations of the mean.

Let me know if you'd like a deeper explanation of these results or any specific calculations!

### Follow-up Questions:
1. What is the z-score formula and how is it applied in normal distributions?
2. How does the empirical rule apply to different standard deviations (1, 2, and 3)?
3. Can you explain how to use the normal distribution table to find exact percentages?
4. What is the significance of 2.5 standard deviations in statistics?
5. How do you determine whether data is normally distributed?

### Tip:
Always round percentages or other statistical answers to the required number of decimal places to match the problem's instructions!

What is the minimum percentage of commuters in New Orleans that have a commute time within 1, 2, and 2.5 standard deviations of the mean? The mean commute time is 25.8 minutes, and the standard deviation is 6.2 minutes. The commute time within 2.5 standard deviations of the mean lies between 13.4 minutes and 38.2 minutes.

Learn how to calculate the minimum percentage of commuters in New Orleans with commute times within 1, 2, and 2.5 standard deviations of the mean using the Empirical Rule. The mean commute time is 25.8 minutes, with a standard deviation of 6.2 minutes. This problem covers key statistical concepts and is suitable for students in Grades 9-12.

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