The square root rule by simulation

You will write the rule for the standard error of a sample share, check it with a simulation, and use it to plan the size of a sample.

The idea. The standard error of a sample share is $\sqrt{\dfrac{p(1 - p)}{n}}$. A simulation makes many samples, finds the share in each, and measures how much the shares spread.

Your tasks.

1. Finish se_rule(p, n). Return $\sqrt{\dfrac{p(1 - p)}{n}}$.
2. Finish simulated_spread(p, n, repeats). Make repeats samples. In each, count how many of n random numbers are below p, and divide by n. Return statistics.pstdev of the shares.
3. Finish size_for(p, target). Return the smallest whole n for which se_rule(p, n) is at most target.