Math Problem Statement

You run quality control for a bolt producer.    This past week, the plant completed a run of 3-inch diameter bolts with mean of 3.02 inches and standard deviation of 0.04 inches.   If a customer’s equipment cannot use bolts greater than 3.07 inches, how many bolts of their recent 550,000 3-inch bolt shipment would you expect to be returned?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics
Normal Distribution
Z-Score

Formulas

Z-Score Formula: z = (x - μ) / σ
Expected Value: Proportion × Total

Theorems

Empirical Rule
Standard Normal Distribution

Suitable Grade Level

Grades 10-12