In a Euclidean space defined by the multivariate normal distribution, what fraction of all points falls within or are tangent to (as opposed to falling outside of) the n-sphere whose center is at the origin and which is tangent to the point p represented by Cartesian coordinates:

vector(θ) =(θ₁, θ₂, θ₃, θ₄ θ₅, ... θ_n)

representing sigmas in the multivariate normal distribution in n dimensions?

This is a post-doctoral question and I could not find it in the literature. I tried searches for the terms you see in the subject line.

p.s. in terms of the picture in the link, the question is: "what fraction of all the dots are in the green circle?" (where in this case the green circle is defined by an arbitrary point on its circumference.)

In terms of R-programming-language code I would like to give a vector and get back a number between 0 and 1.