Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was five minutes. How large a sample should be taken to estimate the meantime for previews at movie theaters to within 90 seconds (1.5 minutes) with 90% confidence?

Amathematical approximation called the rule of 70 tells us that the number of years that it will take something that is growing to double in size is approximately equal to the number 70 divided by its percentage rate of growth. thus, if mexico's real gdp per person is growing at 7 percent per year, it will take about 10 years(=70/7) to double. apply the rule of 70 to solve the following problem. real gdp per person in mexico in 2005 was about $11,000 per person, while it was about $44,000 per person in the u. s. if real gdp per person in mexico grows at the rate of 5 percent per year: how long will it take mexico's real gdp per person to reach the level that the united states was at in 2005? (hint: how many times would mexico's 2005 real gdp per person have to double to reach the u. s.'s 2005 real gdp per person?

Beta coefficients and the capital asset pricing model personal finance problem katherine wilson is wondering how much risk she must undertake to generate an acceptable return on her porfolio. the risk-free return currently is 4%. the return on the overall stock market is 14%. use the capm to calculate how high the beta coefficient of katherine's portfolio would have to be to achieve a portfolio return of 16%.

Afactory owner wants his workers to produce as many widgets as they can so he pays his workers based on how many widgets they produce. however, in order to make sure that the workers do not rush and produce a large number of poorly made widgets, he checks the widgets at random at various stages of their manufacture. if a defect is found in a widget, the pay of the entire section of the factory responsible for that defect is docked. how is this factory owner seeking to solve the agency conflict problem in this case?