There isn't enough given information to solve this problem.
I don't think we can answer this without knowing what kind of distribution we're talking about. Yes, talking about 68% (1 standard deviation in a standard normal distribution) and 99% (around 3 standard deviations in a standard normal distribution) makes it sound like we're talking about some kind of normal distribution, but the problem doesn't state that. We could have a piecewise distribution. The problem does not state the maximum score. With the possibility of a piecewise distribution, the remaining 32% of the scores could have been perfect scores or all 0's, so the only way to be certain of capturing 99% of the scores, the range would have to be 0 to a perfect score. We can't calculate the median (mean) either, because we don't know how many of the remaining 32% of the scores are above or below the given 68% in the 70 to 80 range.