Question

1. The table below gives the probability model for the distribution of total household income in the United States. Total Household Income Under $25,000 $25,000 to $49,999 $50,000 to $74,999 $75,000 to $99,999 S100,000 or over Probabilit 0.223 0.188 0.138 0.179 0.272 Table 1. Total household income (from March 2012 Supplement, Current Population Survey) a. Check to see whether the probability model in Table 1 is legitimate. Explain what you checked b. What is the probability that a randomly chosen household will have a total income less than $100,000? c. What is the probability that a randomly chosen household will have a total income of at least $75,000? d. Suppose a random sample of two U.S. households is selected. What is the probability that both households will have total incomes under $25,000? e. Suppose a random sample of two U.S. households is selected. What is the probability that at least one of the households will have total incomes under $25,000?

Answer 1

a) Total = 0.223 + 0.188 + 0.138 + 0.179 + 0.272 = 1

Since the sum of probabilities is 1, so the probability model in Table 1 is legitimate.

b) Probability = 1 - 0.272 = 0.728

c) Probability = 0.179 + 0.272 = 0.451

d) Probability = (0.223)^2 = 0.0497

e) Probability = 0.223 * (1 - 0.223) + (1 - 0.223) * 0.223 + (0.223)^2 = 0.3963