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on the leeward side of the island of Oahu, in the small village of Nanakuli, abo

ID: 3049195 • Letter: O

Question

on the leeward side of the island of Oahu, in the small village of Nanakuli, about 73% of the must meet until you encounter the first person of Hawailian ancestry in the village of Nanakul residents are of Hawaian ancestry. Letn·1, 2, 3, r-present the number of people you (a) write out a formula for the probability distribution of the random variable n. (use and n in your answer.) P(n) (b) Compute the probabilities that n 1, n = 2, and n-3. (Use 3 decimal places.) P(2) P(3) c) Compute the probability that n 2 4. (Use 3 decimal places.) teiM ar, engde (d) In waikiki, it is estimated that about 17% of the residents are of Hawailan ancestry. Reput party (a), (b), and (c) (a) P(n)

Explanation / Answer

a) This is geometric distribution with p = 0.73

P(n) = (1 - p)n-1 * p = 0.27n-1 * 0.73

b) P(1) = 0.271-1 * 0.73 = 0.73

P(2) = 0.272-1 * 0.73 = 0.197

P(3) = 0.273-1 * 0.73 = 0.053

c) P(n > 4) = 1 - P(X < 4)

                  = 1 - (P(1) + P(2) + P(3))

                  = 1 - (0.73 + 0.197 + 0.053)

                  = 0.02

d) p = 0.17

i) P(n) = (1 - p)n-1 * p = 0.83n-1 * 0.17

ii) P(1) = 0.831-1 * 0.17 = 0.17

P(2) = 0.832-1 * 0.17 = 0.141

P(3) = 0.833-1 * 0.17 = 0.117

ii) P(n > 4) = 1 - P(X < 4)

                  = 1 - (P(1) + P(2) + P(3))

                  = 1 - (0.17 + 0.141 + 0.117)

                  = 0.572