# 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 ___.

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:51 pm ad1c9bdddfhttps://brainmass.com/statistics/probability-theory/chebyshev-s-theorem-14194

#### 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 ___.