SOLUTION: Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test scor

Question 675430: Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 102.5 and 97.5.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is between 102.5 and 97.5.
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Comment: Those are sample means so you have to use 20/sqrt(150) as the
standard deviation.
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z(102.5) = (102.5-100)/[20/sqrt(150)] = 1.5309
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z(97.5) = (97.5-100)/(20/sqrt(150)) = -1.5309
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P(102.5 < x-bar <97.5) = P(-1.5309 < z < 1.5309) = 0.8742
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Cheers,
Stan H.
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