What can be said about the overlap of two probability distributions Suppose I have information about the following two normal distributions:
Red   { Mean = 7.4, Std = .501 }
Green { Mean = 9.7, Std = .465 }

What can be stated about the overlapping area depicted in the diagram below:

The area of overlap is 9%.
The question I am trying to answer is whether the likelihood that the true value of the Green in the population is greater than the true value of the Red in the population.
I'd like to be able to make a claim along the lines of: There is at least a 91% likelihood that Green is greater than Red in the population. Is that claim accurate?
What is the statistical meaning or explanation of this overlap in this context?
Edit: I simplified the question and removed extraneous information. Hopefully its clearer.
 A: In order for the overlap to have meaning, it would have to be relevant to some hypothesis or question about data.
To do that let us assume a context to make an example. Assuming that a Monte Carlo simulation using the displayed means and standard deviations and normal distributions were used to make a histogram, we would be generating a mixture distribution, if we did not sort by color. In that case, the overlapping tail areas would add in those histogram categories, and modern methods that find distributions would have little trouble segregating that mixture into two normal distribution models to recover the input values.
That would not tell us which color was which, but it would correctly identify that two normal distributions produced the histogram. Similarly, if we wanted to do t-testing, we could, and that would identify that the populations have different mean values, and if we did Levene's test for differences of variance, we could then do that test.   
As it stands, the overlap you show means little. A mixture distribution more naturally has different sample sizes in each sub-population of that mixture, i.e., $\mathrm{pdf}_{mixture}=p N(\mu_1,\sigma_1^2)+(1-p)N(\mu_2,\sigma_2^2)$, where $0<p<1$. Assuming a 1/3 Red and 2/3 Green mixture this would look like

For which the relative likelihood of the Red to Green probability components on a log plot would look like:

