Math Problem Statement

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Sampling Distribution
Normal Distribution
Z-scores
Central Limit Theorem

Formulas

Standard Error of the Mean (SEM) = σ / √n
Z-score formula: Z = (X - μ) / SEM
Probability: P(Z1 < Z < Z2) = P(Z2) - P(Z1)

Theorems

Central Limit Theorem

Suitable Grade Level

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