Question 179239:
Chebyshev's theorem and the empirical rule
A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 47.8. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.
a) according to chebyshevs theorem, at least (56%, 75%, 84%, 89% pick one) of the scores lie within 1.5 standard deviations of the mean 47.8
b) Suppose that the distribution is bell-shapped. If approximatly 95% of the scores lie between 28.4 and 67.2, then the approximate value of the standard deviation for the distribution, according to the empirical rule is __
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80. In a recent year, the national mean score for the writing section was 47.8. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.
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Chebyshev Th.: At least [1 - (1/K^2)]% of data lies within K standard
deviations of the mean.
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a) according to chebyshevs theorem, at least (56%, 75%, 84%, 89% pick one) of the scores lie within 1.5 standard deviations of the mean 47.8
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For K = 1.5 you get [1 - 1/(1.5)^2]% = [1-1/2.25]=[1-(4/9)] = 5/9 = 55.5%
Rounding you would get 56%
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b) Suppose that the distribution is bell-shapped. If approximatly 95% of the scores lie between 28.4 and 67.2, then the approximate value of the standard deviation for the distribution, according to the empirical rule is __
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6 sigma = (67.2-28.4) = 38
sigma = 6.47
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Cheers,
Stan H.
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