This page explains what we are doing when we take a 90% confidence interval, and we get a mean and a standard deviation from it.
For normals
module Normal = {
//...
let from90PercentCI = (low, high) => {
let mean = E.A.Floats.mean([low, high])
let stdev = (high -. low) /. (2. *. 1.6448536269514722)
#Normal({mean: mean, stdev: stdev})
}
//...
}
We know that for a normal with mean and standard deviation ,
We can now look at the quantile of a . We find that the 95% point is reached at . (source (opens in a new tab)) This means that the 90% confidence interval is , which has a width of .
So then, if we take a and we multiply it by , it's 90% confidence interval will be multiplied by the same amount. Then we just have to shift it by the mean to get our target normal.