Math Problem Statement

A manufacturer knows that their items have a normally distributed length, with a mean of 17.8 inches, and standard deviation of 3.1 inches.

If one item is chosen at random, what is the probability that it is less than 13.9 inches long?

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Normal Distribution

Formulas

Z = (X - μ) / σ
P(X < x) using Z-table or calculator

Theorems

Empirical Rule for Normal Distribution
Properties of Z-scores

Suitable Grade Level

Grades 9-12