# How to estimate the confidence interval using sample average and sample size ONLY? [duplicate]

Now, I have a sample of $N$ from the population and I know the bad rate of this sample as $b$. The question is can I calculate the confidence interval based on $N$ and $b$ ONLY? In other words, can I calculate the confidence interval $x$ such that with, say, 95% confidence the population bad rate falls in $[\text{range}_1,\text{range}_2]$, where $\text{range}_1$ will be $b-x$ and $\text{range}_2$ will be $b+x$.
• As long as $np(1-p)$ is not small (bigger than 10 is usually plenty), you can use the normal interval described here. If the $n$ is small and $p$ is very near 0 or 1, you may need to consider one of the other binomial approximate confidence intervals. Many other posts here cover aspects of CIs for binomial proportions; the search bar turns many up. – Glen_b Oct 13 '13 at 6:36