Math Problem Statement
A multiple-choice test consists of 30 questions with possible answers of a, b, c, d. Estimate the probability that with random guessing, the number of correct answers is at least 12.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Normal Approximation
Formulas
Binomial probability: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Mean: μ = np
Standard deviation: σ = √(np(1 - p))
Z-score: Z = (X - μ) / σ
Theorems
Central Limit Theorem (for normal approximation)
Suitable Grade Level
Grades 11-12
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