For each of the following situations, explain whether the conditions hold for the sampling distribution of P^1 - P^2 to be approximately normal:
a. A polling organization wants to compare the proportions of men and women who favor a particular candidate in an upcoming election and plans to take random samples of 1000 men and 1000 women.
b. A researcher plans to take a random sample of 500 children and compare the proportion of them who live with both parents in the household to the proportion who live with just one parent in the household.
c. A company builds an expensive component for automobiles and wants to compare two methods of manufacturing them. The company plans to take a random sample of ten of the components manufactured by using each method and compare the proportion of them that fail from each of the two methods.