In 2002, the scores of men on the Math SAT followed theN(534,113) distribution. Women's Math SAT scores that year had theN(500,113) distribution.

The mean Math SAT score for men was 34 points, i.e., 6.8% higher.

The standard deviation of Math SAT score in neither group changed in 2003; the mean score in each group changed in such a way that the mean score for men was 6% higher than the mean score for women.

If the chance of a randomly selected man outscoring a randomly selected woman on Math SAT by more than 70 points in 2003 was 0.405553, what was the mean score for women that year?