Given a sample of data that contains only the score frequency distribution for scores below a certain threshold, is it possible to fit a complete normal distribution so to estimate what the will be the frequency for scores above the threshold.
If I understand this question correctly, you are given something like:
27 people got a 22
32 people got a 23
and told that the distribution is Normal and you are asking how to estimate the distribution so as to find out how many people got above the highest score in the frequencies you are given.
First, of course, such scores are not continuous, but let's suppose there are so many potential scores that we can pretend they are continuous (as is commonly done, e.g. with IQ scores). Let's also take it as given that the distribution is close to Normal (a rather tenuous assumption, but let's assume).
Second, given all the above, fitting a Normal curve to the truncated data becomes an exercise in curve fitting. This has been discussed a bunch here before, and the only general answer is "your ability to do this is going to depend on how much data you are given".