My bad.. I should have said "cone". Basically, I am asking if I have a volume of air in space and a gas is normally distributed in that 3 dimensional space ( aka cone shape, x,y and z), How do I calculate its volume using SAS. Does that make sense?
Although in principle, the volume is infinite since there is always the probability, albeit infinitesimal, that a particle can be arbitrarily as far as desired. It is a gas, after all. I was still thrown by the cone idea.
Are you suggesting that if (X,Y,Z) are the position of a particular gas particle in space, that X,Y,Z are independent identically distributed normal?
For example, in a 2-d curve we are looking for the area under the curve that is associated with say alpha = 0.90. I am loking for the volume of gas under a cone that is in three dimensional space and normally distributed.
So to answer your question... Yes. The position of a particle is independent identically distributed normal. Thus if we had a cloud of the gas particles, they would form a cloud/cone of gas that has the 3-d shape of a normal curve. I want to find the volume of that gas with 90 % confidence.