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The World Bank records the prevalence of HIV in countries around the world. According to their data, "Prevalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV." In one country, the prevalence of HIV is 18.3%. Let X = the number of people you test until you find a person infected with HIV. Part (8) Sketch a graph of the distribution of the discrete random variable X. RX = X) P(X = X) 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.00 012 3 4 5 6 7 8 9 10 11 17 1317 0.00 0123 4 5 6 7 8 9 10 11 12 13 17 P(X = X) P(X = X) 0.15 0.15 0.05 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Part (b) What is the probability that you must test 34 people to find one with HIV? (Round your answer to four decimal places.) Part (c) What is the probability that you must ask nineteen people? (Round your answer to four decimal places.) Part (d) Find the mean and standard deviation of the distribution of X. (Round your answers to four decimal places.) (i) mean (ii) standard deviation