Math Problem Statement
A certain consumer organization reports the number of major defects for each new automobile that it tests. Suppose that the number of such defects for a certain model is a random variable with mean 3.2 and standard deviation 2.4. Among 100 randomly selected cars of this model what is the probability that the average number of defects exceeds 4.
0.0004
0.0098
0.00755
0.0008
Clear selection
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Sampling Distribution
Z-scores
Central Limit Theorem
Formulas
Standard Error: σ_X̄ = σ / √n
Z-score: Z = (X̄ - μ) / σ_X̄
Probability from Z-score: P(Z > z)
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 11-12, College Introductory Statistics
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