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People end up tossing 12% of what they buy at the grocery store. Assume this is the true population proportion and that you plan to take a sample survey of 510 grocery shoppers to further investigate their behavior.

(a) What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion? (Round your answer to four decimal places.)

(b) What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion? (Round your answer to four decimal places.)

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