(adsbygoogle = window.adsbygoogle || []).push({}); Binomial distribution/confidence question for dummies

(The 'dummy' would be me.)

I have an event that happens with unknown probability p. Each of n independent events results in k of these events happening. How do I construct a (95%) confidence interval for p?

For small n it's easy to figure this out with numerical combinatorics:

Pr(at most k events) = [tex]\sum_{i=0}^k{n\choose i}p^i(1-p)^{n-i}[/tex]

Pr(at least k events) = [tex]\sum_{i=k}^n{n\choose i}p^i(1-p)^{n-i}[/tex]

and then find the roots of Pr(at most k events) - 0.05 and Pr(at least k events) - 0.05. (Maybe I should use 0.025 instead?)

But for large n (even not all that large!), this is inconvenient. Surely there is some standard statistical method for this? Sticking as close to the roots as possible would be best -- I'd prefer to use as little Central Limit Theorem as I can.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Distribution/confidence question for dummies

**Physics Forums | Science Articles, Homework Help, Discussion**