A large state university sends recruiters throughout the state to recruit graduating high school seniors to enroll in the university. University records show that 25% of the students who are interviewed by the recruiters actually enroll. If last spring the university recruiters interviewed 1,889 graduating seniors, what is the probability that at least 500 of them will enroll this fall?

Use a normal distribution to compute the required probabilities also state the assumptions necessary for a binomial distribution, and indicate whether the assumptions are reasonable.