well you can play with numbers however you want, to make yourself feel better.
let's say you want to be 95% confident that you'll be accepted to at least one school. also, let's make a conservative estimate that you have a 40% chance, once interviewed, of being accepted to a particular school.
then simply do 0.6^n<0.05 in this case n=6.
realistically, i'd be pretty confident with 4 though, althought i'm sure there're some people on SDN who would say otherwise.