Math Problem Statement
In a sampling a large number of parts manufactured by a machine, the mean number of defectives in a sample of 20 is 2. Out of 1000 such samples, how many would be expected to contain at least 3 defective parts?
Solution
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Math Problem Analysis
Mathematical Concepts
Binomial Distribution
Probability
Sampling
Formulas
Mean of binomial distribution: μ = n * p
Binomial probability formula: P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)
P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12
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