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...

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.

a)      Two people are selected at random from those over age thirty. What is the chance that the average of their two incomes is over $65,000?

b)     One person is selected at random from those over thirty, and independently, one person is selected at random from those under thirty. What is the chance that the younger’s income exceeds the older’s?

c)      What is the chance that the smaller of the two incomes in b) exceeds $50,000?