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 se

Question 1158700: 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
52.0, with a standard deviation of 10.3
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's theorem, at least ___% of the scores lie between 31.4 and 72.6 .
(b) According to Chebyshev's theorem, at least ___% of the scores lie between 26.25 and 77.75 .
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ___% of the scores lie between 31.4 and 72.6 .
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between ___and___.

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Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. is between +/- 2 sd . Chebyshev's says that 1-(1/sd^2) will be within this range for certain, and that is 1-(1/4) or 3/4.
b. is between +/- 2.5 sd. This means that (1- 1/6.25) will be within this range for certain, or 0.84 of the values
c. would be 95% for 2 sd s
d. would b +/- 1 sd s or between 41.7 and 62.3 (52.0+/-10.3)
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