I know the 25th and 75th percentiles of SAT scores for students admitted to a given university, and I want to interpolate over those two points in order to estimate all the percentiles (i.e. 1st-100th) of scores for students admitted to the university.
What I know about SAT score distributions:
- SAT scores must be in the interval [600, 2400] and are approximately normally distributed on a nationwide basis:
Some extremely competitive universities, such as MIT and Harvard, may have the highest possible SAT score (i.e. a 2400) at their 75th percentile, so I'm guessing their distribution might be truncated on the right side (not sure if this would still be a normal distribution?).
I have a histogram of all 1,547,990 SAT scores taken in 2010 including the mean and standard deviation: http://professionals.collegeboard.com/profdownload/sat-percentile-ranks-composite-cr-m-w-2010.pdf.