Question

Mr. Banks gives his class a very difficult practice exam. Each question answered incorrectly is -2 points, and every question answered correctly is +2 points. Sam got a score of -8, and Wallace got a score of -10. Which of the following best compares these scores?

Option 1: Sam did better on the exam than Wallace because -8 > -10.
Option 2: Sam did better on the exam than Wallace because -8 < -10.
Option 3: Wallace did better on the exam than Sam because -10 > -8.
Option 4: Wallace did better on the exam than Sam because -10 < -8.

Answer 1

Sam did better on the exam than Wallace because his score of -8 is greater than Wallace's score of -10, indicating that Sam has a less negative, and therefore higher, score.

Step-by-step explanation:

In the situation described, we must compare two negative numbers to determine who performed better on the practice exam, which is similar to comparing which z-score indicates a better position in relation to a mean score. For scoring, such as on exams or GPA, higher values are indicative of better performance. Therefore, a less negative score means better performance.

Comparing Sam's score of -8 to Wallace's score of -10, we can conclude that:

1. Sam did better than Wallace because -8 is greater than -10.
2. Therefore, Option 1 is the correct comparison: Sam did better on the exam than Wallace because -8 > -10.

This reasoning aligns with how we interpret z-scores, where a z-score that is less negative is closer to the mean and thus indicates better performance relative to others.