Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 82% 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. P(n) =

(b) Compute the probabilities that n = 1, n = 2, and n = 3. (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).

(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. (Round your answer to the nearest whole number.) residents