A recent Harvard study shows that approximately 12% of Americans are left‑handed. Suppose Alex takes a random sample of four Americans. What is the probability that at least one American is left‑handed or at least three Americans are right‑handed?

Answer:A. The probability of at least one American is left-handed is 92.68% for a sample of 4 random Americans.B. The probability of at least three Americans are right-handed is 7.32% for a sample of 4 random AmericanStep-by-step explanation:This is a binomial distribution study where n = 4 and p = 0.12. Using the binomial table, where the first column is the distribution function, f(x), and the second is the cumulative distribution function F(x), we can calculate the probabilities.0 0.5997 0.5997 1 0.3271 0.9268 2 0.0669 0.9937 3 0.0061 0.9998 4 0.0002 1.0000 Now, we can answer the questions, this way:A. What is the probability that at least one American is left‑handed?P (0) + P (1) = 0.5997 + 0.3271 = 0.9268The probability of at least one American is left-handed is 92.68% for a sample of 4 random Americans.B. What is the probability that at least three American are right‑handed?1 - P(0) - P(1) = 1 - 0.5997 - 0.3271 = 0.0732The probability of at least three Americans are right-handed is 7.32% for a sample of 4 random Americans.