If there's a 30% chance that someone will fall within the designated "average" range
Why would you assume there's only a 30% chance of that someone would fall within the middle 30 per cent of the range? That would only be true if we assumed for some reason that people would be uniformly distributed throughout the range.
and assuming the dimensions are roughly independent
Given that the dimensions all concern the physical size of the candidates I don't see why anyone would expect them to be independent. Someone that is very tall would, I assume, also be quite likely to have a long sleeve length for example.