Math Problem Statement
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.2 years, and standard deviation of 1.3 years.
If 6 items are picked at random, 10% of the time their mean life will be less than how many years?
Give your answer to one decimal place.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Z-Score
Sampling Distribution
Formulas
Standard error of the mean = σ / √n
Z-score = (X̄ - μ) / (σ / √n)
X̄ = μ + (Z * (σ / √n))
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 11-12, College Level
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