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 is15.2%. LetX= the numberof people you test until you find a person infected with HIV.

• Part (a)Sketch a graph of the distribution of the discrete random variableX.
• Part (b)What is the probability that you must test30people to find one with HIV? (Round your answer to four decimal places.)
• Part (c)What is the probability that you must askthirteenpeople? (Round your answer to four decimal places.)
• Part (d)Find the mean and standard deviation of the distribution ofX. (Round your answers to four decimal places.)(i) mean (ii) standard deviation