In many problems, we need to determin= e a binomial probability (e.g. probability of a flood in a certain week of = the year), or a proportion (e.g. the proportion of components that are made= to a certain tolerance). To estimate the probability or proportion p you w= ill have had some trials n, of which s were successes. This section describ= es three methods:

The crudest method, not recommended, but explained so you know why to av= oid it.

Normal approximation to the binomial distribution= method

Commonly used. It offers some improvement over the binomial method, but =
still cannot be applied when *s* =3D 0 or *n*, and gives inco=
rrect results at extremes.

*Mid-p *cumulative confidence constru=
ction

The best method that works for all values of s and n. It is also closely aligned to Bayesian results. Useful when we don't know i= f the Binomial outcome is present.