Probability of getting an outlier in a normal distribution

Question

Given $ N $ data points that fit a normal distribution, what is the probability that the $ N+1^{th} $ data point is further away from the mean of the distribution than the previous $ N $ data points?

Answer 1

If the $N$ points and the parameters $\mu, \sigma$ of the distribution are given, find the distance $r$ of the farthest point from $\mu$, and the probability is $2 \Phi(-r/\sigma)$. If the $N$ points are not given, any ordering of the distances of the $N+1$ points are equally likely, so $1/(N+1)$.