North Carolina is about 2.5 times smaller than Oman.

Oman is approximately 309,500 sq km, while North Carolina is approximately 126,161 sq km, making North Carolina 40.76% the size of Oman. Meanwhile, the population of Oman is ~3.8 million people (5.8 million more people live in North Carolina).
Tip: This to-scale comparison of Oman vs. North Carolina uses the Mercator projection, which distorts the size of regions near the poles.