A math professor once claimed that 90% of students pass a particular class of hers.To check this claim, a random sample of 150 students who had taken this class was obtained.It was found that 129 passed the class.If the professor is correct, what is the probability that 129 or fewer of the students in such a sample would have passed the class?
A) 0.9484
B) 0.0516
C) 0.5516
D) 0.4484

Question

Quizplus · Accepted Answer

The sample size is n = 150, and the probability of passing the class is p = 0.9. The number of students who passed the class in the sample is X = 129. We can use the binomial distribution to model this situation, which has the following formula:

P(X ≤ 129) = Σi=0^129 (150 choose i) * (0.9)^i * (0.1)^(150-i)

Using a calculator or software, we can find that P(X ≤ 129) is approximately 0.0516. Therefore, the probability that 129 or fewer students in such a sample would have passed the class is 0.0516 or 5.16% (option B).

A Math Professor Once Claimed That 90% of Students Pass