A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of 20 to 80.  

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 47.2, with a standard deviation of 9.7. 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 ?56%75%84%89% of the scores lie between 27.8 and 66.6.

(b) According to Chebyshev’s theorem, at least ?56%75%84%89% of the scores lie between 22.95 and 71.45.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the scores lie between 27.8 and 66.6.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the scores lie between and .

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