I think this is a pretty correct approximation. An even better way is to assume vectors are uniformly distributed on the sphere. The dot product has expectation

I think this is a pretty correct approximation. An even better way is to assume vectors are uniformly distributed on the sphere. The dot product has expectation 0 and the variance is 1/300 (cf http://stats.stackexchange.com/questions/85916/distribution-of-a-scalar-product-of-two-random-unit-vectors-in-mathbbrd http://stats.stackexchange.com/questions/85916/distribution-...). Chebyshev's inequality shows that the probability that the dot product be greater than 0.3 in absolute value is less than 4%.