Math Problem Statement

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 147147 millimeters, and a variance of 2525.

If a random sample of 4444 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 1.11.1 millimeters? Round your answer to four decimal places.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Central Limit Theorem
Normal Distribution
Z-Scores

Formulas

Standard Error of the Mean (SEM) = σ / √n
Z = (X̄ - μ) / SEM
P(|Z| > 1.324) = 2 × P(Z > 1.324)

Theorems

Central Limit Theorem

Suitable Grade Level

College Statistics or Advanced High School (Grades 11-12)