2.44 Income and gender: The relative frequency table below displays the distribution of annual total personal income (in 2009 inflation-adjusted dollars) for a representative sample of 96,420,486 Americans. These data come from the American Community Survey for 2005-2009. This sample is comprised of 59% males and 41% females.
| Income | Total Percentage |
|---|---|
| $1 to $9,999 or loss | 2.2% |
| $10,000 to $14,999 | 4.7% |
| $15,000 to $24,999 | 15.8% |
| $25,000 to $34,999 | 18.3% |
| $35,000 to $49,999 | 21.2% |
| $50,000 to $64,999 | 13.9% |
| $65,000 to $74,999 | 5.8% |
| $75,000 to $99,999 | 8.4% |
| $100,000 or more | 9.7% |
a) Describe the distribution of total personal income:
b) What is the probability that a randomly chosen US resident makes less than $50,000 per year? % (please round to two decimal places, ie. xx.xx%)
c) What is the probability that a randomly chosen US resident makes less than $50,000 per year and is female? % (please round to two decimal places, ie. xx.xx%)
d) The same data source indicates that 71.8% of females make less than $50,000 per year. What could explain the discrepancy between this number and the number you calculated in part c)?