As was discussed in the Analytics in Action from Chapter 2, the U.S. Census Bureau is a leading source of quantitative data related to the people and economy of the United States. The cross tabulation below represents the number of households (1,000s) and the household income by the highest level of education for the head of household (U.S. Census Bureau web site, 2013). Use this cross tabulation to answer the following questions.

a. Develop a joint probability table.
b. What is the probability the head of one of these households has a master's degree or higher education?
c. What is the probability a household is headed by someone with a high school diploma earning $100,000 or more?
d. What is the probability one of these households has an income below $25,000?
e. What is the probability a household is headed by someone with a bachelor's degree earning less than $25,000?
f. Are household income and educational level independent?

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Household Income Highest Level of Education High school graduate 9,880 Bachelor's degree Master's degree Doctoral degree Under $25,000 to $50,000 to $100,000 $25,000 $49,999 $99,999and Over Total 3,482 32,773 7,817 22,131 9,003 1,076 1,737 16,46965,644 9,970 4,164 1,205 160 15,499 9,441 /,666 3,019 422 20,548 2,484 685 79 4,094 Total 13,128