3. Describing Data Numerically
Interpreting Standard Deviation
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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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Verified step by step guidance1
Identify the key components of the problem: the sample mean (312 pages), the standard deviation (26 pages), and the percentage of data to be included in the central range (95%).
Recall the Empirical Rule, which states that for a normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ).
Calculate the lower bound of the range by subtracting 2 times the standard deviation from the mean: Lower Bound = μ - 2σ. In MathML:
Calculate the upper bound of the range by adding 2 times the standard deviation to the mean: Upper Bound = μ + 2σ. In MathML:
Combine the lower and upper bounds to express the central range containing 95% of the books: (Lower Bound, Upper Bound).
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