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

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1. Introduction to Statistics53m
2. Describing Data with Tables and Graphs2h 1m
3. Describing Data Numerically1h 48m
4. Probability2h 26m
5. Binomial Distribution & Discrete Random Variables2h 55m
6. Normal Distribution & Continuous Random Variables1h 48m
7. Sampling Distributions & Confidence Intervals: Mean1h 17m
- Introduction to Confidence Intervals
  22m
- Confidence Intervals for Population Mean
  55m
8. Sampling Distributions & Confidence Intervals: Proportion1h 20m
- Sampling Distribution of Sample Proportion
  35m
- Confidence Intervals for Population Proportion
  45m
9. Hypothesis Testing for One Sample1h 8m
- Steps in Hypothesis Testing
  1h 8m
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 30m
14. ANOVA1h 4m

3. Describing Data Numerically

Interpreting Standard Deviation

Statistics for Business

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. Find the percentage of books in the sample with less than 338 pages using the Empirical Rule of Standard Deviation.

$84 percent sign$

$34 percent sign$

$50 percent sign$

$16 percent sign$

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Verified step by step guidance

Identify the key information provided in the problem: the sample mean (312 pages), the standard deviation (26 pages), and the value of interest (338 pages). The problem also specifies the use of the Empirical Rule, which applies to data that follows a normal distribution.

Recall the Empirical Rule: approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. This rule helps estimate the percentage of data within specific ranges.

Calculate how many standard deviations the value 338 is from the mean. Use the formula for the z-score:

z = \frac{x - μ}{σ}

, where

x

is the value of interest (338),

μ

is the mean (312), and

σ

is the standard deviation (26).

Interpret the z-score using the Empirical Rule. Determine the percentage of data below the value of 338 by summing the percentages within the relevant standard deviation ranges. For example, if the z-score is 1, approximately 68% of the data falls within 1 standard deviation, and half of that (34%) is above the mean. Add this to the 50% below the mean to find the total percentage below 338.

Compare the calculated percentage to the provided answer choices (84%, 34%, 50%, 16%) and select the closest match. This step ensures the solution aligns with the problem's context and the Empirical Rule.

7:51m

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Struggling with Statistics for Business?

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.

Watch next

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