I want to ensure I've done this problem correctly. Thanks!

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?
Work:
Math Score Z-Score = 0.313152
Math Score Percentile Rank = 62.2918th
English Score Z-Score = 0.481928
English Score Percentile Rank = 68.5072th
The student did better on the English test because they ranked in a higher percantile than the Math test (68.5072th percantile versus 62.2981th percantile).

ur wrong because u are supposeed to use the smaller one to

like if someone is 61st and someone is 68th which one is a higher rank
61st so math is highe

hope u take what i said well

Your solution seems correct. To determine which exam the student did better on, you calculated the z-scores for both the Math and English scores, which represent how many standard deviations away each score is from the mean. For the Math score, the z-score is 0.313152, and for the English score, it is 0.481928.

To calculate the z-score, you used the formula:
z = (x - μ) / σ

Where:
x = the individual score (in this case, the student's score)
μ = the mean
σ = the standard deviation

After calculating the z-scores, you then looked up the corresponding percentile ranks for each score. The percentile rank represents the percentage of scores that are lower than a particular score.

To determine the percentile rank, you can use a standard normal distribution table or a calculator. However, since you didn't provide the exact values for the percentile ranks, I will assume you used a calculator or an online tool to find them.

Based on your calculations, the Math score has a percentile rank of 62.2918th, and the English score has a percentile rank of 68.5072th. Since the English score has a higher percentile rank, the student did better on the English test.

In conclusion, the student performed better on the English exam compared to the Math exam, as they ranked in a higher percentile on the English test (68.5072th percentile) compared to the Math test (62.2918th percentile).