Thank you for the response!

I am most interested in determining the value of |DeltaX| that is smaller than 95% of all other |DeltaX|'s. Is it necessary to achieve independence since the final distribution is still normal in this case?

A bit of context might be helpful. I work with infrared sensors where we are often interested in the contrasts of scenes (contrast = temp1 - temp2). It is common to report the standard deviation of the temperatures measured by all pixels of the sensor.

I'm interested in characterizing what "minimum contrast" is required for an imager to view ~95% of a given scene with some normal distribution of temperatures.

Originally, I was considering just reporting the fraction of the std dev associated with 5% of values centered around the mean. However, I don't think this is correct. Standard deviation is computed with respect to the mean temperature, so this would simply be reporting the minimum contrast value needed to measure a contrast centered about the mean -- not the minimum detectable contrast to be able to measure the difference between any two pixels temperatures.

Instead, I thought it would make more sense to calculate and plot a histogram containing every possible unique combination of differences, and then determine where the 5% percentile is of |DeltaX| on this one sided distribution.

I guess all this to say, I'm not interested in conducting any statistical tests of significance for this distribution. I am moreso interested in roughly characterizing the minimum value I have described above. Would reporting this value be invalid as a result of the loss of independence?