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# Finding lower and upper limits based on a known distribution

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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 49.6, with a standard deviation of 10.9. Based on this information, complete the following statements about the distribution of the scores on the writing section for the recent year.

1. According to Chebyshev's theorem, at least what percent of the scores lie between 27.8 and 71.4?
2. According to Chebyshev's theorem, at least 89% of the scores lie between _ and _ (round your answer to 1 decimal place.)
3. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between _ and _
4. Suppose that the distribution is bell-shaped. According to the empirical rule approximately what percent of the scores lie between 27.8 and 71.4?