SOLUTION: 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 sur

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Question 476447: 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 540 grocery shoppers to further investigate their behavior.
a.Show the sampling distribution of (p), the proportion of groceries thrown out by your sample respondents (to 4 decimals)?


b.What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)?


c.What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. the sampling distribution of proportions would be normally distributed, N%28p%2C+sqrt%28%28pq%29%2Fn%29%29, or N(0.12,0.014). mu+=+0.12, and sigma+=+0.014.
b. we want the probability under the standard normal table between
z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+0.03%2F0.014+=+2.14 and
z+=+%28P+-+p%29%2Fsqrt%28%28pq%29%2Fn%29+=+-0.03%2F0.014+=+-2.14
==> P%28-2.14+%3C+z+%3C+2.14%29+=+0.9838+-+0.0162+=+0.9676
c. this follows the same procedure as in (b).