According to a survey, approximately 69% of US adults believe that they have achieved, or are within reach of, the "American Dream" (that is, home ownership and financial stability). Assume that the true proportion of all US adults who have reached or are optimistic about reaching the American Dream is p=0.69. Now consider a random sample of 500 US adults. Complete parts a and b below.
What is the probability that between 61% and 72% of the sampled adults believe they have reached or are optimistic about reaching the American Dream? The probability is (Round to three decimal places as needed.)



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