In a certain college, 33% of the math majors belong to foreign student. If 10 students are selected at random from the math majors, that is the probability that no more than 6 are foreign?
A) 0.9815
B) 0.913
C) 0.9846
D) 0.0547

Question

Quizplus · Accepted Answer

The probability that a student is a foreign student is 0.33, and the probability that a student is not a foreign student is 0.67. To find the probability that no more than 6 out of 10 students are foreign, we calculate the probability of having 0 to 6 foreign students and sum these probabilities. This can be done using the binomial probability formula, which is P(X = k) = (nCk) * (p^k) * ((1-p)^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and (nCk) is the combination of n items taken k at a time. The sum of these probabilities for k = 0 to 6 gives approximately 0.9815, indicating that there is a 98.15% chance that no more than 6 out of 10 randomly selected students are foreign.

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