Past exam of the probability, statistics and options I course of the University of Oxford / 2009 / O / 2 / iii

The relation $N=k/p$ is strictly decreasing. Thus an interval $0<L<U<1$ transforms by reversing endpoints:Keep integer population sizes satisfying $N>k$. If the clipped lower confidence endpoint for $p$ is zero, the transformed upper endpoint for $N$ is infinite. This monotone transformation preserves the approximate coverage probability supplied by the interval for $p$.