Math Problem Statement

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?

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Empirical Rule
Z-Score

Formulas

Empirical Rule: 68% of data lies within one standard deviation of the mean
Z-Score Formula: z = (x - μ) / σ

Theorems

Empirical Rule
Properties of Normal Distribution

Suitable Grade Level

Grades 10-12