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. Find the percentage of books in the sample with less than 338 pages using the Empirical Rule of Standard Deviation.
3. Describing Data Numerically
Interpreting Standard Deviation
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.
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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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