In a study, 39% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, 3 or fewer are in excellent health.
A)0.1877
B)0.1256
C)0.0667
D)0.1210

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 successes, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. In this case, n = 13, p = 0.39 (the probability of an adult reporting excellent health), and we are interested in the probability of k = 0, 1, 2, or 3 successes. We calculate the probability for each of these values of k and sum them to find the total probability of 3 or fewer successes. The correct answer, after performing these calculations, is 0.1877, indicating that there is an 18.77% chance that in a random sample of 13 adults from this area, 3 or fewer will report their health as excellent.

In a Study, 39% of Adults Questioned Reported That Their