Rory from Alaska wrote in a comment:
I guarantee you that she has at least a 120 IQ.
You simply do not survive in Alaska politics unless you are extremely intelligent and streetwise.
From the recent biography on her:
Sarah had two childhood traits that her family says played trajectory roles in her life. From the time she was in elementary school, she consumed newspapers with a passion. “She read the paper from the very top left hand corner to the bottom right corner to the very last page,” said Molly. “She didn’t want to miss a word. She didn’t just read it—she knew every word she had read and analyzed it.”
Sarah preferred nonfiction to the Nancy Drew books that her classmates were reading. In junior high school, Heather— a year older in school—often enlisted Sarah’s help with book reports. “She was such a bookworm. Whenever I was assigned to read a book, she’d already read it,” Heather said.
If she really was a bookworm when she was a kid, and really liked to read the newspaper when she was in elementary school, that’s very promising. It does indicate an IQ higher than the average graduate of the University of Idaho.