Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Z-scores
Percentiles
Linear Transformations

Formulas

Z-score formula: z = (x - μ) / σ
Percentile calculation: x = μ + zσ
Linear transformation: new score = a + b(old score)

Theorems

Properties of Normal Distribution
Linear transformation of random variables

Suitable Grade Level

Grades 11-12