Hi,

So, I am wondering how do I find that scale factor exactly in order to have for example 95% confidence level?

The (adapted) α can be taken from the following table. The last column refers to the quantile used to scale the confidence interval to the desired probability.

And do my standard deviations for x, y and z represent only 20% confidence level?

Each single standard deviation represents a confidence level of about 68 %. However, the following plot shows two confidence regions as ellipses having identical standard deviations.

Obviously, both ellipses are different, so they cannot have an identical confidence level.

/Micha