Math Problem Statement
The lengths of nails produced in a factory are normally distributed with a mean of 4.814.81 centimeters and a standard deviation of 0.050.05 centimeters. Find the two lengths that separate the top 10%10% and the bottom 10%10%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Percentiles
Z-scores
Formulas
x = μ + z * σ
Theorems
Properties of the Normal Distribution
Z-score Conversion
Suitable Grade Level
Grades 10-12
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