So I know this may be basic but I'm having trouble piecing together the right formulas and logic to understand this. Most of the Z-tables online seem to have different information than the one provided to us so I've left the table below. Its a centered Z-table and not a left tail one.
For first year students at a university the correlation between SAT scores and first year GPA is 0.60. The scatter diagram is football shaped. Predict the first year GPA for a student whose percentile rank on the SAT was 30%.
In order to get the proper z-score I subtracted the remaining percent twice from 100%. I dont follow the logic behind this but apparently it works. |100 - 70 - 70| = 40%. The z score corresponding to 40% of the area on our table is ~.53
I then multiplied by the correlation to get ~0.32 (this makes sense to me). This corresponds to about 25%. I'm not quite sure how to then get this number back into percentile. The answer is 38%.