In recent analyses of Census figures, one in four American counties has passed or is approaching the tipping point where black, Hispanic, and Asian children constitute a majority of the under-20 population (New York Times , August 6, 2008). Racial and ethnic minorities now account for 43% of Americans under 20.
a. What is the expected number of under-20 whites in a random sample of 5,000 Americans? What is the corresponding standard deviation?
b. What is the expected number of racial and ethnic minorities in a random sample of 5,000 under-20 Americans? What is the corresponding standard deviation?
c. If you randomly sample six American counties, what is the probability that for the under-20 population, whites have a clear majority in all of the counties?