Explain the general rationale behind using a z-score for describing how an individual performed on an exam compared to just stating the overall mean and the individual's score. How does the information differ in the two situations? What additional information are you gaining with a z-score?
Imagine you are in charge of reviewing applications for your academic institution. As a preliminary measure, you want to review only the top 25% of applicants on the basis of standardized test scores. How does calculating the z-score provide additional information regarding how each subject did overall? Provide specific examples of how you would use the information and interpret the scores.