11 College Admissions A small liberal arts college in Ohio would like to have an entering class of 450 students next year Past experience shows that about 37 of the students admitted will decide to attend The college is planning to admit 1175 students Suppose that students make their decisions independently and that the probability is 0 37 that a randomly chosen student will accept the offer of admission a What are the mean and standard deviation of the number of students who accept the admissions offer from this college b Use the Normal approximation to approximate probability that the college gets more students than it wants Be sure to check that you can safely use the approximation c Use software or an online binomial calculator to compute the exact prob ability that the college gets more students than it wants How good is the approximation in part b d To decrease the probability of getting more students than are wanted does the college need to increase or decrease the number of students it admits Using software or an online binomial calculator what is the larg est number of students that the college can admit if administrators want the exact probability of getting more students than they want to be no