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Chebyshev's Theorem

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.
1. According to Chebyshev's theorem, at least 36% of the scores likes between ___ and ___ (Round your answer to 1 decimal place.)

2. According to Chebyshev's theorem, at least ___ of the scores lie between 29.4 and 72.2.
a. 56%
b. 75%
c. 84%
d. 89%
3. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ___ of the scores lie between 29.4 and 72.2.
a. 68%
b. 75%
c. 95%
d. 99.7%

4. 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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Solution Summary

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.
1. According to Chebyshev's theorem, at least 36% of the scores likes between ___ and ___ (Round your answer to 1 decimal place.)

2. According to Chebyshev's theorem, at least ___ of the scores lie between 29.4 and 72.2.
a. 56%
b. 75%
c. 84%
d. 89%
3. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ___ of the scores lie between 29.4 and 72.2.
a. 68%
b. 75%
c. 95%
d. 99.7%

4. 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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