In a Time Magazine/Aspen Ideas Festival poll conducted by Penn Schoen Berland during June 1–8, 2011, Americans age 18 years and older were asked, “Overall, do you think the past decade has been one of progress or decline for the U.S. as a country?” Of the respondents, 68% said decline (Time, July 11, 2011). Assume that this result is true for the current population of American adults.

a. Find the probability that in a random sample of 1000 American adults, the proportion who will say decline in response to the aforementioned question is

i. Greater than .70

ii. Between .66 and .71

iii. Less than .65

iv. Between .695 and .715

v. Less than .69

vi. More than .67

b. What is the probability that in a random sample of 1000 American adults, the proportion who will say decline in response to the aforementioned question is within .025 of the population proportion?

c. What is the probability that in a random sample of 1000 American adults, the proportion who will say decline in response to the aforementioned question is not within .03 of the population proportion?

d. What is the probability that in a random sample of 1000 American adults, the proportion who will say decline in response to the aforementioned question is greater than the population proportion by .02 or more?