Answer:To determine which class Nonhlanhla should expect the better grade, we need to compare her scores in both exams relative to the mean and standard deviation of each class.
For the Math exam:
- Mean (μ) = 40
- Standard Deviation (σ) = 5
- Nonhlanhla's score (X) = 45
To compare her score with the class performance, we can use the Z-score formula:
Z = (X - μ) / σ
For Nonhlanhla's Math score:
Z_math = (45 - 40) / 5
Z_math = 1
A Z-score of 1 means Nonhlanhla's score is 1 standard deviation above the mean of the Math class.
For the Science exam:
- Mean (μ) = 60
- Standard Deviation (σ) = 8
- Nonhlanhla's score (X) = 68
To compare her score with the class performance, we calculate the Z-score for her Science score:
Z_science = (68 - 60) / 8
Z_science = 1
Similarly, a Z-score of 1 for the Science exam means Nonhlanhla's score is 1 standard deviation above the mean of the Science class.
Since both of Nonhlanhla's scores are 1 standard deviation above the mean in their respective classes, it indicates that she performed relatively better in the Science exam. Generally, being one standard deviation above the mean indicates that the student's score is higher compared to a significant portion of the class, and in this case, it applies to both exams. However, since the standard deviation for the Science exam (8) is larger than that of the Math exam (5), Nonhlanhla's score of 68 in Science carries relatively more significance and is comparatively better than her score of 45 in Math. Therefore, Nonhlanhla should expect the better grade in the Science class.