We believe that 86% of the population of all Calculus I students consider calculus an exciting subject. Supposewe randomly and independently selected 29 students from the population. If the true percentage is really 86%,find the probability of observing 28 or more of the students who consider calculus to be an exciting subject inour sample of 29.
A) 0.072098
B) 0.012602
C) 0.059495
D) 0.927902

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, and p is the probability of success on a single trial. Here, n = 29, p = 0.86, and we are interested in k = 28 and k = 29. The probability of observing exactly 28 students who consider calculus exciting is calculated using the binomial formula, and similarly for 29 students. The total probability of observing 28 or more students is the sum of these two probabilities. The correct answer is obtained by performing these calculations, which results in a probability of approximately 0.072098.

We Believe That 86% of the Population of All Calculus