# Chebyshev's Theorem

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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 ___.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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