In a large corporation, people over age thirty have an annual income whose distribution can be approximated by a normal distribution with mean 60,000 and standard deviation 10,000. The incomes of those under age thirty are also approximately normal, but with mean 40,000 and standard deviation 10,000. One person is selected at random from those over thirty, and independently, one person is selected at random from those under thirty.
a) What is the chance that the younger's income exceeds the older?
b) What is the chance that the smaller of the two incomes in a) exceeds 50,000?
For a), you're looking for $P(X_2 -X_1)>0$ , where $X_2$ is the random variable "Salary of population over thirty; similar for $X_1$. You need to figure out how to obtain this distribution ( Hint: find the distribution for -$X_2$, then : what result do you know that is used to find the distribution of a sum of random variables? ). For 2) Find the z-value of $50,000$ and look up a chart for the standard normal.