3. In one elementary school, 200 students are tested on the subject of Math and English. The table below shows the mean and standard deviation for each subject.

Mean SD
Math 67 9.58
English 78 12.45

One student’s Math score was 70 and the same individual’s English score was 84. On which exam did the student do better?

Calculate the two Z scores and compare on normal distribution table (see previous post).

To determine on which exam the student performed better, we can compare the student's scores relative to the mean and standard deviation of each subject.

For Math:

1. Calculate the z-score for the student's Math score using the formula:
z = (x - μ) / σ

where:
x = student's Math score (70)
μ = mean of Math scores (67)
σ = standard deviation of Math scores (9.58)

z = (70 - 67) / 9.58
z = 0.31

2. Interpreting the z-score: A positive z-score indicates that the student's score is above the mean, while a negative z-score indicates that it is below the mean. In this case, the student's Math z-score is positive, which means their score is above the average.

For English:

1. Calculate the z-score for the student's English score using the same formula as before:
z = (x - μ) / σ

where:
x = student's English score (84)
μ = mean of English scores (78)
σ = standard deviation of English scores (12.45)

z = (84 - 78) / 12.45
z = 0.48

2. Interpreting the z-score: Similar to the Math z-score, a positive z-score for the English score indicates that it is above the average.

Based on the z-scores calculated, we can see that the student performed better in English since their z-score for English (0.48) is higher than their z-score for Math (0.31). This means the student's English score is relatively further above the mean compared to their Math score.