I wouldn't interpret it that way at all. First, performing well on a standardized test isn't a reliable indicator of intelligence. All it means is that you did well on the test.
I think the more education one or both parents have, the more likely they will value education in their children and help them develop the skillset to do well in school or on these type of tests.
No you are wrong. As I stated prior to 1975 they were a good predictor of intelligence. They are not now because they have changed the test design. Read "The Bell Curve" and get a clue. The best science we have now is that intelligence does exist and about half of intelligence is heritable.
The problem with your response is that the graph doesn't show the results of just one person. When large numbers of people of the same ethnic/racial backgrounds produce a graph like the one shown, the results are more likely to produce reliable data.