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The problem uses the Empirical Rule and involves a normal distribution of vehicle speeds. Here's the breakdown:

- **Mean speed** = 70 mph
- **Standard deviation (σ)** = 3 mph
- We are asked to estimate the percent of vehicles with speeds between **61 mph** and **79 mph**.

### Empirical Rule (68-95-99.7 Rule)
This rule states that for a normal distribution:
- 68% of data falls within 1 standard deviation (mean ± 1σ),
- 95% falls within 2 standard deviations (mean ± 2σ),
- 99.7% falls within 3 standard deviations (mean ± 3σ).

### Calculating the Range
- **61 mph** is 3 standard deviations below the mean: \( 70 - 3\sigma = 70 - 9 = 61 \).
- **79 mph** is 3 standard deviations above the mean: \( 70 + 3\sigma = 70 + 9 = 79 \).

Thus, the speeds from **61 mph to 79 mph** cover **3 standard deviations** on both sides of the mean. According to the Empirical Rule, **99.7%** of the data falls within this range.

### Answer
Approximately **99.7%** of vehicles travel between 61 mph and 79 mph.

Would you like further details or have any questions?

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Here are five related questions for further understanding:

1. What percentage of vehicles travel between 67 mph and 73 mph?
2. How would the range change if the standard deviation increased to 5 mph?
3. Can you explain why the Empirical Rule applies only to normal distributions?
4. What percentage of vehicles travel faster than 79 mph based on this data?
5. How can we use the Empirical Rule to estimate percentiles in a normal distribution?

**Tip:** The Empirical Rule is a useful tool for quickly estimating data distribution when dealing with normally distributed datasets.

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 61 miles per hour and 79 miles per hour.

Learn how to apply the Empirical Rule to estimate the percent of vehicles traveling between 61 and 79 miles per hour on a highway. The mean speed is 70 mph with a standard deviation of 3 mph, and this problem involves understanding the 68-95-99.7 Rule in a normal distribution.

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