edu/courses/1134474/quizzes/secured\#lockdown 4. 3pts each In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. a) Find the probability that exactly 9 of them have brown eyes. (Please translate the problem and show what you are entering into your calculator)

Step 1 ：Translate the problem: In a region, there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 13 people are randomly selected. We need to find the probability that exactly 9 of them have brown eyes.

Step 2 ：This is a binomial distribution problem. The binomial distribution model is an appropriate statistical model if the following conditions are met: 1. The trials are independent. 2. The number of trials, n, is fixed. 3. Each trial outcome can be classified as a success or failure. 4. The probability of a success, p, is the same for each trial.

Step 3 ：In this case, we have: - n = 13 (the number of people randomly selected) - p = 0.95 (the probability that a randomly selected person has brown eyes) - k = 9 (the number of successes we are interested in, i.e., the number of people with brown eyes)

Step 4 ：The formula for the binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: - \(P(X=k)\) is the probability of k successes in n trials - \(C(n, k)\) is the combination of n items taken k at a time - p is the probability of success on a single trial - n is the number of trials - k is the number of successes

Step 5 ：After calculating, we find that the probability that exactly 9 out of 13 randomly selected people have brown eyes is approximately 0.0028164270497068604.

Step 6 ：Final Answer: The probability that exactly 9 out of 13 randomly selected people have brown eyes is approximately \(\boxed{0.0028}\).