Ok. For the normal probability density function, it is the parameter that "means" the amount of variation around the mean. (See the sigma in the formula for a normal PDF here: https://en.wikipedia.org/wiki/Normal_distribution)
But I don't know what you are getting at? And it's probably going to take me a few days to find time to read the refereed article.
You edited your post to add the diagram and the second question after I responded to it. The most useful answer to your first question is that any normally distributed random variable has a probability of approximately 95% of being within two standard deviations of the mean (if I remember my stat class correctly).
It is customary in science to reject the "null hypothesis" if the results of the measurements are less than 5% likely if the null hypothesis is true.
You edited your post to add the diagram and the second question after I responded to it
and your point? Is that supposed to be a bad thing?
Sometimes I don't think of everything I want to say right off...so I add to it.
Just keeping the record tidy. I will fix typos, but I will put any significant addition in a separate reply. This has several benefits including notifying my correspondent that I have added more in response.
um yeah...
does that mean you're acting as a go-between?
that I'm not really talking to you but that you are an intermediary?
Nope. It just means that sometimes I reread what I have already posted. If there's a typo, I'll fix it. If I want to add something, I'll do it by posting a separate additional reply.