People end up tossing 12% of what they buy at the grocery store (Reader\'s Diges

Question

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 farther investigate their behavior. Show the sampling distribution of (p), the proportion of groceries thrown out by your sample respondents (to 4 decimals)? Can assume to the normally distributed because np > = 5 and n(1-p)> = 3 p = standard error of the proportion O(p) = .0140 What is the probability that your survey will provide a sample proportion within plusorminus.03 of the population proportion (to 4 decimals)? What is the probability that your survey will provide a sample proportion within a plusminus .015 of the population proportion (to 4 decimal)?

Explanation / Answer

a)here p=0.12

std error =(p(1-p)/n)1/2 =0.0140

b)P(0.12-0.03<X<0.12+0.03)=P(-0.03/0.0140<Z<0.03/0.014)=P(-2.1453<Z<2.1453)=0.9839-0.0160=0.9679

c)

P(0.12-0.015<X<0.12+0.015)=P(-0.015/0.0140<Z<0.015/0.014)=P(-1.0714<Z<1.0714)=0.8580-0.0.1420=0.7160

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