If I had to guess, <100 IQ points.
I'd love to say someone so popular with a good segment of the population has a good head on her shoulders, but unfortunately I've listened to her speak too much and it's clear she's just another career politician who can't think for herself. I see a disturbing lack of integrity in addition to the yokel-like fundie ignorance she seems to be proud of.
I don't see anything in her academic career that makes her stand out either, which affirms what she's already done and said to prove she isn't qualified to run a burger joint, let alone a lofty government office.
I'm all for a strong, smart woman taking a turn running the country. But the notion of Palin being that woman is just bad, nee, HORRIBLE comedy. I think women in general should be especially outraged. There are far better representatives of double Xs to choose, conservative or otherwise.
Edit: Forgot to mention, I feel there is a difference between being "smart" and being "clever."