Math Problem Statement
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 195-cm and a standard deviation of 0.6-cm. For shipment, 25 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is between 194.7-cm and 194.9-cm. P(194.7-cm < M < 194.9-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Normal Distribution
Central Limit Theorem
Z-scores
Formulas
z = (M - μ_M) / σ_M
σ_M = σ / √n
P(a < M < b) = P(z_2) - P(z_1)
Theorems
Central Limit Theorem
Suitable Grade Level
College-level or Advanced High School Statistics
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