Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 3 - Data Description - 3-2 Measures of Variation - Exercises 3-2 - Page 146: 41


$474-554$, $2.5\%$

Work Step by Step

Empirical rule: • Approximately 68% of the data values will fall within 1 standard deviation of the mean. • Approximately 95% of the data values will fall within 2 standard deviations of the mean. • Approximately 99.7% of the data values will fall within 3 standard deviations of the mean. 41. SAT Scores The national average for mathematics SATs in 2011 was 514. Suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was approximately 40. Within what boundaries would you expect 68% of the scores to fall? What percentage of scores would be above 594? We can use the empirical rule for this bell-shaped distribution. $68\%$ corresponds to within 1 standard deviation which means the boundaries are $514-40$ to $514+40$ or $474-554$. A score of 594 corresponds to $\frac{594-514}{40}=2$ standard deviations (SD), within 2SD we have $95\%$ of the data and $1-0.95=0.05$ will be outside, so there will be half or $0.025$ above 594.
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