2
QuizMultiple Choice

Binomial Distribution — Quiz

Question 2 • Algebra II

Mrs. Gomes found that 40 percent of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth. cap p times k successes is equal to n cap c sub k p to the k th power open paren 1 minus p close paren raised to the n minus k power n cap c sub k is equal to the fraction with numerator n factorial and denominator open paren n minus k close paren factorial times k factorial

Answer
A
0 point 0 0 5
B
0 point 2 1 3
C
0 point 0 0 8
D
0 point 2 2 7

Explanation

Use the binomial formula with n = 12 students, k = 4 successes, and p = 0.40: P(X = 4) = ₁₂C₄(0.40)⁴(0.60)⁸. Since ₁₂C₄ = 495, the probability is about 0.21284, which rounds to 0.213. The correct choice is 0.213.

AI-written and checked against the verified answer.

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