Find the indicated probability. Round to four decimal places.
-In a study, 35% 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 10 adults randomly
Selected from this area, only 3 reported that their health was excellent. Find the probability that
When 10 adults are randomly selected, 3 or fewer are in excellent health.
A)0.5138
B)0.2522
C)0.3743
D)0.2616

Question

Find the indicated probability. Round to four decimal places.
-In a study, 35% 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 10 adults randomly
Selected from this area, only 3 reported that their health was excellent. Find the probability that
When 10 adults are randomly selected, 3 or fewer are in excellent health. 
A)0.5138
B)0.2522
C)0.3743
D)0.2616

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 given trial. In this case, n = 10, p = 0.35, and we are looking for the probability of k = 0, 1, 2, or 3 successes. Calculating each of these probabilities and summing them gives us the total probability of 3 or fewer successes, which rounds to 0.5138.

Find the Indicated Probability