Percentile Rank Comparison Between Two Groups

A statistical analysis was performed on the test scores of two distinct groups of students, Group A and Group B, on a standardized exam. The following statistics were calculated:

• Group A:
• Mean: 78
• Standard Deviation: 10
• Group B:
• Mean: 85
• Standard Deviation: 15

Assuming that both groups are normally distributed, determine which group has a higher percentile rank for the same raw score of 85.

To evaluate the percentile rank, you can use the Z-score formula:

$$Z = \f\frac{X - \mu}{\sigma}$$

where $X$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation.