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People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March...

People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 100 grocery shoppers to further investigate their behavior. What is the probability that the sample will provide a sample proportion within ±0.03 of the population proportion? Round intermediate calculations to four decimal places if necessary. Express your answer as a decimal rounded to four decimal places.

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Answer #1

Solution

=  [p ( 1 - p ) / n] = [(0.12 * 0.88) / 100 ] = 0.0325

= P[ -0.03 / 0.0325 < ( - ) / < 0.03 / 0.0325]

= P(-0.92 < z < 0.92)

= P(z < 0.92) - P(z < -0.92)

= 0.9424

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