You can definitely use a Bayesian analysis to solve your problem. You have $k$ categories, the observed number of answers for each category are $(x_1,\dots,x_k)$, and your likelihood is proportional to
$$
  \theta_1^{x_1} \dots \theta_k^{x_k} \, ,
$$
where $\theta_i$ is the proportion of users of the library that belong to category $i$. You don't know the $\theta_i$'s (they are parameters), but if you suppose that *a priori* they are distributed uniformly on the $k$-simplex, then, given the $x_i$'s, the $\theta_i$'s are distributed *a posteriori*  as
$$
  (\theta_1,\dots,\theta_k) \mid (x_1,\dots,x_k) \sim \textrm{Dirichlet}(x_1 + 1, \dots, x_k + 1) \, .
$$
From this posterior distribution, you can compute virtually anything that interests you, like credible intervals for the $\theta_i$'s, the probability that you have more college students than grad students, etc. Just do a simple Monte Carlo of the posterior using [R][1]. If you need some sample code, please post a piece of your data, and we will help you.

  [1]: http://www.r-project.org/