SOLUTION: 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 sect

Question 178972: 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 50.4. 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 Chebyshev theorem, at least (56%,75%,84% 89% Pick which one) or the scores lie within 2 standard deviations of the mean 50.4.
B)Suppose that the distribution is bell-shaped. If approximatly 68% of the scores lie between 40.5 and 60.3, 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 50.4. 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 Chebyshev theorem, at least (56%,75%,84% 89% Pick which one) or the scores lie within 2 standard deviations of the mean 50.4.
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89%
Check Chebyshev's Theorem using Google
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B)Suppose that the distribution is bell-shaped. If approximatly 68% of the scores lie between 40.5 and 60.3, then the approximate value of the standard deviation for the distribution, according to the empirical rule is
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That means 40.5 and 60.3 are each one standard deviation away from the mean.
That means the mean is (60.3+40.5)/2 = 100.8/2 = 50.5
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Cheers,
Stan H.

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