A study compares the daily caloric intake of two different populations. Population 1 has mean $$\mu_1 = 2200$$ calories with standard deviation $$\sigma_1 = 400$$ calories. Population 2 has mean $$\mu_2 = 1900$$ calories with standard deviation $$\sigma_2 = 350$$ calories. If independent random samples of size $$n_1 = 64$$ and $$n_2 = 49$$ are selected, what is the probability that the sample mean from Population 1 exceeds the sample mean from Population 2 by at least 350 calories?