Suppose that we have two normal populations with the means and standard deviations listed here. If random samples of size 25 are drawn from each population, what is the probability that the mean of sample 1 is greater than the mean of sample 2?
Population 1: mean = 40 and SD = 6
Population 2: mean = 38 and SD = 8
This solution finds the distribution of the difference of two sample means and then uses that distribution find the desired probability.