Math Problem Statement

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

(b) What is the 20 percentile of the distribution of test scores, rounded to three decimal places?

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Z-Score
Percentiles

Formulas

Z = (X - μ) / σ
X = μ + Z * σ

Theorems

Properties of the Normal Distribution
Standard Normal Distribution

Suitable Grade Level

Grades 10-12