Question 1

The average gas mileage of 50% of the cars is most likely represented by the interval of 24 to 32 miles per gallon.

This interval captures a reasonable range for average gas mileage, including many cars that fall within typical efficiency levels.

A) 20 to 32

While this range includes some vehicles with lower mileage, it is broader than necessary for capturing the average of 50% of cars. The inclusion of lower mileage values (below 24 mpg) makes this option less precise for the average.

B) 24 to 32

This interval is most accurate as it targets a specific and common range of mileage that aligns well with the average performance of many cars. It effectively captures the midpoint of typical gas mileage, making it the best choice for representing 50% of cars.

C) 29 to 32

This range is too narrow and does not encompass a sufficient variety of vehicles. It primarily focuses on higher mileage cars and excludes many that would fall below 29 mpg, thus failing to represent the average of 50%.

D) 30 to 44

This option is overly broad at the upper end, including vehicles that achieve higher mileage. While it may cover a wider array of efficient cars, it does not accurately reflect the average range for the majority of vehicles, particularly those that achieve lower mileage.

E) 32 to 44

This interval focuses exclusively on higher mileage cars and excludes many vehicles that fall below 32 mpg. As such, it does not represent the average gas mileage for 50% of the cars effectively.

Conclusion

The option B (24 to 32) is the most representative of the average gas mileage for 50% of cars, as it strikes a balance between lower and higher mileage vehicles. All other options either include too broad a range, target too narrow a segment, or focus on higher mileage cars, thus failing to accurately capture the average for the majority.