The Normal Distribution · Superchallenge problem

In a town, adult women's heights are normal with mean $164$ cm and standard deviation $6$ cm, and adult men's heights are normal with mean $178$ cm and standard deviation $7$ cm. There are equally many adult women and men. An adult chosen at random turns out to be taller than $175$ cm. What is the probability that this adult is a woman? Round to three decimal places.