A train has 200 seats. Suppose that the mean weight of men is 180 pounds with a standard deviation of 25 and the mean weight of women 170 is with a standard deviation of 15. Assume that all the seats in trains are always occupied, there are always 100 men and 100 women on the train and that the weight of different passengers are independent random variables.

Find the probability that when you randomly pick a train, the mean weight of people on it is greater than 174 pounds.