According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage

Question:

According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distribution of the sample proportion? Why or why not?

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