The problem in the image asks to estimate the percentage of vehicles whose speeds are between 59 miles per hour (mph) and 67 mph, using the Empirical Rule (also known as the 68-95-99.7 rule). Here are the details:

• Mean speed: 63 mph
• Standard deviation: 4 mph
• Speeds to estimate: Between 59 mph and 67 mph
• Assumed data distribution: Normal distribution (bell-shaped)

Applying the Empirical Rule:

1. The Empirical Rule states that:

   • 68% of the data falls within 1 standard deviation of the mean.
   • 95% of the data falls within 2 standard deviations of the mean.
   • 99.7% of the data falls within 3 standard deviations of the mean.

2. Mean ± 1 standard deviation:

   • Mean: 63 mph
   • 1 standard deviation = 4 mph, so:
     • Lower bound = 63 - 4 = 59 mph
     • Upper bound = 63 + 4 = 67 mph

Since 59 mph and 67 mph are exactly 1 standard deviation below and above the mean, we can use the Empirical Rule. The percentage of vehicles with speeds between 59 mph and 67 mph is approximately 68% of the total data.

Final Answer:

Approximately 68% of vehicles travel between 59 mph and 67 mph.

Would you like more details on this explanation or have any further questions?

Here are five related questions you could explore next:

1. What percentage of vehicles travel between 55 mph and 71 mph?
2. How does the Empirical Rule change for data that is not normally distributed?
3. What percentage of vehicles travel faster than 67 mph?
4. How would you calculate the percentage of vehicles between 63 mph and 71 mph?
5. How can the Empirical Rule be applied in real-world traffic studies?

Tip: When using the Empirical Rule, always check if the data follows a normal distribution (bell curve), as the rule applies best under that assumption.