ABC News reports that 58% of U.S. drivers admit to speeding. Suppose that a new satellite technology can instantly measure the speed of any vehicle on a U.S. road and determine whether the vehicle is speeding, and this satellite technology was used to take a random sample of 20,000 vehicles at 6 p.m. EST on a recent Tuesday afternoon. 

a. For this investigation, what is the sampling distribution for sample proportion of vehicles on U.S. roads that speed? 

b. What is the probability that the sample proportion of speeders p̅ will be within 1% of the population proportion of speeders? 

c. Suppose the sample proportion of speeders p̅ differs from the U.S population proportion of seeders by more than 1%? How would you interpret this result?