According to a Pew Research Center nationwide telephone survey of American adults conducted by phone between March 15 and April 24, 2011, 25% of American college graduates said that their student loans make it harder for them to buy a home . Suppose that this result is true for the current population of American college graduates. Let be the proportion in a random sample of1000 American college graduates who will say that their student loans make it harder for them to buy a home. Find the probability that the value of is:
a. Within .02 of the population proportion
b. Not within .02 of the population proportion
c. Greater than the population proportion by .025 or more
d. Less than the population proportion by .03 or more
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