I'm using these, which came directly from my host in an email:
Path To Convert: /usr/bin/convert
Path To Mogrify: /usr/bin/mogrify

I also tried:
/usr/lib/convert
/usr/lib/mogrify

Could it be a permissions issue on one of my directories?

Everything seems to be functioning fine on my board, but I do get some "fail" readings when I check permissions in CP. What directory would effect the Captcha image?