Find a beta distribution that fits your desired confidence interval
Here is a tool for finding a beta distribution that fits your desired confidence interval. E.g., to find a beta distribution whose 95% confidence interval is 0.2 to 0.8, input 0.2, 0.8, and 0.95 in their respective fields below:
The virtue of using a a beta distribution is that it is inherently bounded between 0 and 1, and thus much more suitable for estimating things like probabilities, and, more speculatively, ranges of values. Previously, various people in my extended social circle, including myself, had been using lognormals (bad, because not bounded) or truncated lognormals (better, but deeply inelegant) for those purposes. I hope that with this tool such practices will come to and end.
You can read more about how this utility works here. Advanced users will particularly enjoy the npm package.
This is a project of the Quantified Uncertainty Research Institute.