Question 759341: Assume that the population proportion of all business professionals who select an airline based on price is 0.25. A random sample of 250 business professionals is to be taken for further study.
A) What is the shape, mean (expected value), and standard deviation of the sampling distribution of the sample proportion for samples of size 250?
B) What is the probability that our sample of 250 results in a sample proportion that falls within 4 percent (+/- .04) of the population value?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume that the population proportion of all business professionals who select an airline based on price is 0.25. A random sample of 250 business professionals is to be taken for further study.
A) What is the shape, mean (expected value), and standard deviation of the sampling distribution of the sample proportion for samples of size 250?
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Ans: shape = normal ; mean = np = 250*0.25 = 62.5 ; std = sqrt[0.25*0.75/250] = 0.0274
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B) What is the probability that our sample of 250 results in a sample proportion that falls within 4 percent (+/- .04) of the population value?
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z(0.25-0.04) = z(0.21) = (0.21-0.25)/0.0274 = -1.46
z(0.25+0.04) = z(0.29) = (0.29-0.25)/0.0274 = 1.46
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P(condtion met) = P(-1.46< z < 1.46) = normalcdf(-1.46,1.46) = 0.8557
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Cheers,
Stan H.
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