Refer to Exercise 7.79. Beginning in the second half of 2011, there were widespread protests in many American cities that were primarily against Wall Street corruption and the gap between the rich and the poor in America. According to a Time Magazine/ABT SRBI poll conducted by telephone during October 9–10, 2011, 86% of adults who were familiar with those protests agreed that Wall Street and lobbyists have too much influence in Washington (The New York Times, October 22, 2011). Assume that this percentage is true for the current population of American adults. Let p̂ be the proportion in a random sample of 400 American adults who hold the opinion that Wall Street and lobbyists have too much influence in Washington. Find the probability that the value of p̂ will be
a. Greater than .88
b. Between .82 and .84