If we are saying the passing score is 74, then the way to attack this problem would be to say that: the area from 74 onward is 2103/7685=.273. In that case, then we do 1-.273=.726, which is the percentage of students that failed. So then we can use the z-score table, and find that the z-score in the100(* .726)% percentile is 0.6. Then to get our z-score, we know that z= x-u/sd, which we already have. So our formula looks like this:
0.6=74-u/16.62
16.62*0.6=74-u
9.972=74-u
u=74-9.972
u=64.02.
If that doesn't answer this question, I don't know what will. I don't know if you were saying that 74 was the passing score or that the weighted average for those that passed was 74. If it is the latter, then I would need more information, such as the baseline for the passing score. Hopefully this helps though!
