Math Problem Statement
A drug test is accurate 97% of the time. If the test is given to 1600 people who have not taken drugs, what is the probability that at most 50 will test positive?
Probability =
Solution
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Math Problem Analysis
Mathematical Concepts
Binomial Distribution
Normal Approximation
Central Limit Theorem
Probability
Formulas
Binomial distribution formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Normal approximation: X ~ N(μ = np, σ^2 = np(1 - p))
Z-score formula: z = (X - μ) / σ
Theorems
Central Limit Theorem
Normal Approximation to Binomial Distribution
Suitable Grade Level
Grades 10-12
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