Define the mean of these 1,000 scores as the person's "true"
score. On some tests, the person will have scored below the "true"
score; on these tests the person was less lucky than average. On some
tests the person will have scored above the true score; on these tests
the person was more lucky than average. Consider the ways in which someone
could score 750. There are three possibilities: (1) their "true"
score is 750 and they had exactly average luck, (2) their "true"
score is below 750 and they had better than average luck, and (3) their
"true" score is above 750 and they had worse than average luck.
Consider which is more likely, possibility #2 or possibility #3. There
are very few people with "true" scores above 750 (roughly 6
in 1,000); there are many more people with true scores between 700 and
750 (roughly 17 in 1,000). Since there are so many more people with true
scores between 700 and 750 than between 750 and 800, it is more likely
that someone scoring 750 is from the former group and was lucky than from
the latter group and was unlucky.