Since the number of trials is not fixed, N is neither a binomial or a geometric variable, it is an inverse binomial variable.
The sample is chosen at random, hence, the trials are independent, that is, each person has the same probability of answering it, hence N is not a geometric variable.
For it to be a binomial distribution, there needs to be a fixed number of trials, which there is not, hence, N is also not a binomial variable.
A similar problem is given at https://brainly.com/question/25644451