Math Problem Statement

In the 2000 census, the so-called “long form” received by one of every six households contained 52 questions, ranging from your occupation and income all the way to whether you had a bathtub. According to the U.S. Census Bureau, the mean completion time for the long form is 38 minutes. Assuming a standard deviation of 5 minutes and a simple random sample of 50 persons who filled out the long form, what is the probability that their average time for completion of the form was more than 45 minutes?

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Sampling Distribution
Central Limit Theorem

Formulas

Standard Error (SE) = σ / √n
Z-score = (X̄ - μ) / SE

Theorems

Central Limit Theorem

Suitable Grade Level

College Level