Question 1034316: In a certain city of several million people, 6.4% of the adults are unemployed. If a random sample of 265 adults in this city is selected, approximate the probability that fewer than 14 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity.
Round your answer to at least three decimal places. Do not round any intermediate steps.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a certain city of several million people, 6.4% of the adults are unemployed. If a random sample of 265 adults in this city is selected, approximate the probability that fewer than 14 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity.
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u = np = 0.064*265 = 17.23
std = sqrt(npq) = sqrt(17.23*0.936) = 16.127
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P(x < 14) in binom = P(x < 14.5) in normal approx
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z(14.5) = (14.5-17.23)/16.127 = -0.1693
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P(x < 14.5) = P(z < -0.1693) = normalcdf(-100,-0.1693) = 0.4328
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Cheers,
Stan H.
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