Math Problem Statement
Assume that 12 jurors are randomly selected from a population in which 86% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. 0 0+ 1 0+ 2 0+ 3 0+ 4 0+ 5 0.0004 6 0.0028 7 0.0148 8 0.0569 9 0.1553 10 0.2863 11 0.3197 12 0.1637
Find the probability of exactly 6 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
Find the probability of 6 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
If the the probability of 6 or fewer Mexican-Americans is less than 5% then it is unusual, and suggest that there might be descrmination. Does 6 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? yes no
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Cumulative Probability
Formulas
P(X = k) for binomial distribution: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Cumulative probability: P(X ≤ k) = Σ P(X = i) for i = 0 to k
Theorems
Binomial Theorem
Law of Large Numbers
Suitable Grade Level
Grades 10-12
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