How often do the intervals catch the truth?

You will simulate many surveys from a town where the true share is known, and count how often the 95% interval catches it.

The idea. Each survey asks n people. Each person says yes when a random number is below the true share p. The survey's interval is $\hat p \pm 1.96\sqrt{\dfrac{\hat p(1 - \hat p)}{n}}$.

Your tasks.

1. Finish one_interval(p, n). Simulate one survey and return its interval (low, high).
2. Finish caught(pair, p). Return True when p lies from low to high.
3. Finish coverage(p, n, repeats). Return the share of repeats intervals that catch p.