(I) Airport security uses a randomized selection procedure that flags individuals 5% of the time for additional screening after they pass through a certain checkpoint. Over the course of a day, 60 individuals pass through this particular checkpoint. Among these 60 individuals, let Y be the number that were flagged for additional screening. Can you help me understand what is the most appropriate distribution that can be used to model Y and why?

(II) A political polling agency is interested in estimating the proportion of Missouri voters who have decided not to participate in the upcoming 2020 presidential election. They have enough resources to survey 800 individuals, and aim to use the sample proportion p in their estimate. Can you help me understand what is the most appropriate distribution that can be used to model p and why?

(III) Medical researchers seek to obtain a sample of 5 individuals with a particular genetic trait that is only present in 2% of the population they are studying. They decide to examine individuals from this population one-by-one and test them for this trait until they obtain their desired sample. Interested in estimating the cost of their study, they want to model X = total # of indivduals they examine until they obtain their sample of 5 individuals with this trait. Can you help me understand what is the most appropriate distribution that can be used to model X and why?