In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6
Belong to an ethnic minority? Round to three decimal places.
A)0.982
B)0.913
C)0.055
D)0.985

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. Here, n = 10 (students chosen), p = 0.33 (probability of choosing a student who belongs to an ethnic minority), and we want the probability of choosing no more than 6 students who belong to an ethnic minority, which means we need to calculate the sum of probabilities for k = 0 to k = 6. The calculation is complex and typically requires either a statistical calculator or software. The correct answer, rounded to three decimal places, is 0.982, indicating that there is a 98.2% chance of selecting no more than 6 students who belong to an ethnic minority out of 10 chosen at random.

In a Certain College, 33% of the Physics Majors Belong