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Notes -
This doesn't make sense. It doesn't matter what the score curve is like. You can always transform a scoring system with a 130 min score and 170 max score to one with a 0 min score and 40 max score and the same curve by just subtracting 130 from each score.
You can literally make the numbers do that, yes, but they won't necessarily mean the same thing.
40 is twice as much 20. 170 is not twice as much as 150.
A scale may cut off the tails in either direction after enough standard deviations because it is not able to accurately measure those extremes, or because the testmaker doesn't have any use for measures beyond those limits. In that case, cutting off your scale at 130 properly implies that there's lots of lower numbers you could get but are not measuring; anchoring the bottom of your scale to 0 improperly implies that this is the lower bound of possible performance.
Etc.
Again, I don't know how these scales are designed or what they're supposed to mean. But it's very possible that relationships like these (probably not these specific ones, but other things that do not survive translation) may be intended in their scale.
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