Math Problem Statement

A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 316 and a standard deviation of 44.

What proportion of students taking the exam receive a score that is within 72 points of the mean?

Round your answer to four (4) decimal places. (e.g. 0.1234)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Z-Scores

Formulas

Z = (X - μ) / σ
Proportion = P(a < X < b) where a and b are bounds

Theorems

Empirical Rule (68-95-99.7 Rule)
Properties of the Normal Distribution

Suitable Grade Level

Grades 10-12