I'm not sure you can assume a normal distribution for intelligence. The median will be at 50%, but if the distribution is skewed by the existence of profoundly stupid people, then it's entirely possible that more than 50% of the population has below average intelligence.
As evidence of this possibility, I submit the last Democratic debate and AOC who by themselves probably lower the mean intelligence of the US at least 1% below the median.
I think IQ is defined so as to follow a normal distribution with 100 as the mean, and when you have a very large sample (i.e. US population) these tend to be normal in distribution anyway.