Question 4 In 2014, there were 34,4?5000 persons living in the United States classified as "poor" by economic standards. Of these poor persons, 2S,TOT,000 were native-born [N] and 4,?53,000 were foreign-born [F]. Each person is either native-born or foreign-born. Dur random experiment will be to randomly draw 3 people from this population of poor persons [assume we will replace each person right after we draw them, so that it is possible to draw the same person twice]. a. 'w'hat is the probability that at least one of the individuals that we draw is a foreign-born person? [hint: the complement of this would be "no one I pick is foreign born"] F'[at least one foreign-born person] = b. 'w'hat is the probability of drawing exactly 2 foreign-born persons? F'[exactly tw o foreign-born persons] = Question 5 Over the summer, Chapman University discovers that it has enough beds in the dorms to enroll 12 additional students. Since the University would gain additional revenue with nearly no change in operating costs, it would like to fill those slots. How ever, the University strongly prefers not to end up enrolling more students than it has beds. The University can accept students from the waiting list to fill the open slots. From experience, Chapman knows that the probability that a student offered admission from the waiting list actually enrolls in the college is 40% [the rest choose to go elsewhere - such as STATE -- screw STATE]. a. If admission is offered to 20 students off of the waiting list, what is the expected number of students who will actually enroll? Find what is the variance in the number of students who will enroll? E[enrollments] = variance[enrollments] = b. If admission is offered to 20 students off of the waiting list, what is the probability that exactly 12 students will enroll? F'[12 students enroll] = c. If admission is offered to 20 students off of the waiting list, what is the probability that there will not be enough beds [i.e. that more than 12 students will enroll]? F'[more than 12 students enroll] = d. The University is willing to take some risk that they may enroll more students than they have beds. How ever, they want to be 80% certain that they will have enough beds for all students. Chapman can offer admission to this many students from the wait list