A sample of 500 random adult books in a library has an average of...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

3. Describing Data Numerically

Interpreting Standard Deviation

Statistics

3. Describing Data Numerically

Interpreting Standard Deviation

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Multiple Choice

A sample of 500 random adult books in a library has an average of 312 pages with a standard deviation of 26 pages. According to the Empirical Rule of Standard Deviation, find the central range of page lengths containing 95% of the books in the sample.

$open paren 312 comma 364 close paren$

$open paren 260 comma 312 close paren$

$open paren 260 comma 364 close paren$

$open paren 286 comma 338 close paren$

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Verified step by step guidance

Identify the key components of the problem: the sample mean (312 pages), the standard deviation (26 pages), and the percentage of data to be covered (95%). The Empirical Rule states that 95% of the data falls within 2 standard deviations from the mean in a normal distribution.

Calculate the lower bound of the range by subtracting 2 standard deviations from the mean. Use the formula: Lower Bound = Mean - 2 × Standard Deviation. In MathML:

Lower Bound = Mean - 2 \times Standard Deviation

Calculate the upper bound of the range by adding 2 standard deviations to the mean. Use the formula: Upper Bound = Mean + 2 × Standard Deviation. In MathML:

Upper Bound = Mean + 2 \times Standard Deviation

Combine the lower and upper bounds to form the central range. This range represents the page lengths containing 95% of the books in the sample.

Verify the calculated range against the provided options to identify the correct answer. The correct range should match the interval (260, 364).

7:51m

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Struggling with Statistics?

A sample of 500 random adult books in a library has an average of 312 pages with a standard deviation of 26 pages. According to the Empirical Rule of Standard Deviation, find the central range of page lengths containing 95% of the books in the sample.

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