Math Problem Statement

Researchers have studied the IQ scores of a sample of adults from a population. The distribution of IQ scores is normally distributed with a mean of 100 and standard deviation of 15. What is the percentage of IQ scores below 120? What percentage of IQ scores are between 100 and 120? What percentage of IQ scores are above 85? What IQ score divides the lowest 20% of scores from the highest 80%? What percentage of IQ scores fall between 90 and 110, and between 90 and 130?

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Percentiles
Z-Scores
Probability

Formulas

Z = (X - μ) / σ
Percentile from Z-score tables

Theorems

Empirical Rule
Properties of Normal Distribution

Suitable Grade Level

Grades 11-12, College-level

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