I am working on taking a methodology class and when working on past exams I stumbled over this question. I used n=(z^2∗Var)/error^2 to obtain the variance; however, I have no idea to obtain the probability from that without a mean.

Suppose we are interested in what percentage of students in a group of 10,00010,000 would recommend their school to others. Furthermore, suppose we want to be 99% sure that the error from our sample of respondents is no more than four percentage points and the computed minimum sample size is 373373. What percentage of students did we expect to be willing to recommend their school?

Thanks for any help!