26
practice examMultiple Choice

Practice Exam

Question 26 • 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 at most 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 8
B
0 point 4 3 8
C
0 point 6 6 5
D
0 point 5 6 2

Explanation

Let X be the number of surveyed students who have taken chemistry. This is a binomial setting with n = 12 and p = 0.40, so add the probabilities for k = 0, 1, 2, 3, and 4. Using P(X = k) = C(12, k)(0.40)^k(0.60)^(12 − k), the sum is about 0.438178, which rounds to 0.438. The correct choice is 0.438.

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