Question 864316: 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 ±.015 of the population proportion (to 4 decimals)?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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)?
p = 0.12
s = sqrt[0.12*0.88/540]
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b) What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?
0.12-0.015 = 0.105
z(0.105) = (0.105-0.12)/sqrt[0.12*0.88/540] = -1.0726
0.12+0.015 = 0.135
z(0.135) = +1.0726
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P(-1.0726< z < +1.0726) = normalcdf(-1.0726,1.0726) = 0.7165
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Cheers,
Stan H.
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