Question 630068: A worldwide organization of academics claims that the mean IQ score of its members is 112, with a standard deviation of 15. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 117.2. If the organization's claim is correct, what is the probability of having a sample mean of 117.2 or less for a random sample of this size?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A worldwide organization of academics claims that the mean IQ score of its members is 112, with a standard deviation of 15. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 117.2. If the organization's claim is correct, what is the probability of having a sample mean of 117.2 or less for a random sample of this size?
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z(117.2) = (117.2-112)/[15/sqrt(35)] = 2.0510
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P(x-bar < 117.2) = P(z < 2.0510) = normalcdf(-100,2.0510) = 0.9800
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Cheers,
Stan H.
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