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 sco

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Question 693733: 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 99.5 and 100.5.
Answer by stanbon(75887) About Me  (Show Source):
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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 99.5 and 100.5.
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z(99.5) = (99.5-100)/20 = -0.5/(20/sqrt(150)) = -0.3062
z(100.5) = (100.5-100)/(20/sqrt(150)) = +0.3062
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P(99.5<= x-bar <=100.5) = P(-0.3062<= z <= +0.3062) = 0.2405
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Cheers,
Stan H.
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