@dpiponi I think the analysis in my last reply (https://assemblag.es/@qualmist/113536125549115188) applies here as well – the particular distribution doesn't matter since we're doing order statistics. For a continuous uniform distribution from 0 to 1, the probability distribution will limit to a delta at (3 - √5)/2 ≈ 0.38. To turn this into limit for the standard normal, you apply the inverse CDF of the standard normal to this value, which Mathematica tells me gives "-Sqrt[2] InverseErfc[3 - Sqrt[5]]", aka -0.300321.
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