Use the geometric probability distribution to solve the following problem.

On the leeward side of the island of Oahu, in a small village, about 76% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, ... represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.)

P(n) = ______

(b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.)

P(1) = ______

P(2) = ______

P(3) = ______

(c) Compute the probability that n 4. Hint: P(n 4) = 1 P(n = 1) P(n = 2) P(n = 3). (Enter a number. Round your answer to three decimal places.)

______

(d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)

______residents