Probability question that stumped me completely - reward

[mindless]

Asked of me in an interview today and I couldn't figure it out at all. Given a series that is normally distributed with mean 0 and standard deviation of 1, what is the probability that the next 100 elements will have an average greater than 1.5?

Now, the probability that the next element is greater than 1.5 is simple to find using CDF and a table to look up erf. And finding the probability that the next 100 are all greater than 1.5 is simply p(next > 1.5)^100. However, I'm stumped about looking at the average.

If I'm not missing something obvious, I'd like to email the interviewer and let him know that the question is really tricky, but I'd also like to show him the answer. If someone can help me get the answer, I'll transfer them $25 on pokerstars.