Question

Round probability values to 4 decimal places where applicable. 4. Binomial: Twenty percent of the statistics students stated that they have children (on the introduction survey at the beginning of the semester). You randomly select 10 students from your class. Find the probability that the number of students who have children is A) exactly three, B) more than eight.

Answer 1

To find the probability of a specific number of students who have children and the probability of more than a certain number of students who have children, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that the number of students who have children is exactly three, we can use the binomial probability formula. The formula is P(X = k) = (nCk)(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, and nCk represents the number of ways to choose k successes from n trials. In this case, n = 10, p = 0.2, and k = 3. Plugging in these values, we get P(X = 3) = (10C3)(0.2^3)((1-0.2)^(10-3)).

To find the probability that the number of students who have children is more than eight, we need to find the sum of the probabilities of having nine successes and ten successes. Using the same formula as before and plugging in n = 10, p = 0.2, and k = 9 and k = 10, we get P(X > 8) = P(X = 9) + P(X = 10).