An economic analysis of economic data shows that the annual income of a randomly chosen individual from country A has a mean of $18,000 and a standard deviation of $6,000, and the annual income of a randomly chosen individual from country B has a mean of $31,000 and a standard deviation of $8,000. 100 individuals are chosen at random from Country A and 100 from Country B. Find the approximate probability that the average annual income from the group chosen from Country B is at least $15,000 larger than the average annual income from the group chosen from Country A (all amounts in US$)