(13.36) Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in 2011: Income <15 15−29 30−74 75−199 ⩾200 Probability 0.264 0.218 0.298 0.186 0.034 (a) What is the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more? P(income ⩾ $ 30,000) (±0.001) = (b) Given that a return shows an income of at least $30,000, what is the conditional probability that the income is at least $75,000? P(income ⩾ $ 75,000 | income ⩾ $ 30,000) (±0.001) =

Upscale hotels in the united states recently cut their prices by 20 percent in an effort to bolster dwindling occupancy rates among business travelers. a survey performed by a major research organization indicated that businesses are wary of current economic conditions and are now resorting to electronic media, such as the internet and the telephone, to transact business. assume a company's budget permits it to spend $5,000 per month on either business travel or electronic media to transact business. graphically illustrate how a 20 percent decline in the price of business travel would impact this company's budget set if the price of business travel was initially $1,000 per trip and the price of electronic media was $500 per hour. suppose that, after the price of business travel drops, the company issues a report indicating that its marginal rate of substitution between electronic media and business travel is 1. is the company allocating resources efficiently? explain.

When used-car dealers signal the quality of a used car with a warranty, a. buyers believe the signal because the cost of a false signal is high b. it is not rational to believe the signal because some used-car dealers are crooked c. the demand for lemons is eliminated d. the price of a lemon rises above the price of a good used car because warranty costs on lemons are greater than warranty costs on good used cars

Shawn received an e-mail offering a great deal on music, movie, and game downloads. he has never heard of the company, and the e-mail address and company name do not match. what should shawn do?