A statistics professor has stated that 90% of his students pass the class. To check this claim, a random sample of 150 students who have taken the class indicated that 129 passed the class. If the professor's claim is correct, what is the probability that 129 or fewer will pass the class this semester?
A) .9484
B) .0516
C) .5516
D) .4484
E) .1624

Question

Quizplus · Accepted Answer

We can model this problem using a binomial distribution with n=150 and p=0.9. 
The probability of 129 or fewer students passing can be calculated by finding the cumulative probability up to and including 129:
P(X ≤ 129) = Σ P(X = i) for i = 0 to 129
Using a binomial probability table or calculator, we get:
P(X ≤ 129) = 0.0516
Therefore, the probability that 129 or fewer will pass the class this semester is 0.0516, which corresponds to answer choice B.

A Statistics Professor Has Stated That 90% of His Students