Sigchi4life
Category:
Statistics
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Question description

A nationwide test taken by high school sophomores and juniors has three sections, each scored on a scale of  to . In a recent year, the national mean score for the writing section was , with a standard deviation of . 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 26.8 and 74.8 .

(b) According to Chebyshev's theorem, at least  of the scores lie between 31.6 and 70.0 .

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the scores lie between 31.6 and 70.0 .

(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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