Math Problem Statement

A particular bus route has a population mean time for the trip of 35 minutes with a standard deviation of 12 minutes. You randomly sample 64 routes. What is the probability the sample mean is between 30 and 40 minutes? (Round your final answer to 4 decimal places.)

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics
Central Limit Theorem
Normal Distribution

Formulas

Standard Error: SE = σ / √n
Z-score: z = (x̄ - μ) / SE

Theorems

Central Limit Theorem

Suitable Grade Level

College Level - Introductory Statistics