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%.
Thanks for the help!
Best Answer
You almost got there.
Your 0.32 would more accurately be 0.315 (for number of sd's below the mean). This gives a central area of about 25% and a left tail area of about 38%. More accurately, (100-24.8)/2=37.6 (Your 24.8 is 100-?-? = 24.8 and you want to figure out what that ? value would be)