According to the U.S. Census Bureau, the mean household income in the United States in 2000 was $63,091 and the median household income was $50,054. The variability of household income is quite large, with the 85th percentile (i.e., top 15%) approximately equal to $100,000, and an overall standard deviation of approximately $25,000. Suppose random samples of 225 households were selected.

a) What proportion of the sample means would be below $50,054?

b) What proportion of the sample means would be above $100,000?

c)Why is the probability you calculated in (b) so much lower than 0.15, even though 15% of individual households have incomes above $100,000?

d) If we select random samples of size 20, can we calculate the probabilities requested in (a) and (b)? Explain.