According to a 2014 poll by the American Academy of Ophthalmology, Americans break down like this when it comes to eye color: Brown eyes: 45 % Blue eyes: 27 % Hazel eyes: 18% Green eyes: 9% Other: 1% Consider a random group of 20 American people. Let a random variable X be the number of Americans in this group with green eyes. (a) Argue that this is a binomial experiment. (b) Find the probability that i. None have green eyes ii. Nine have green eyes iii. At most three have green eyes iv. At least four have green eyes v. If four people out of twenty have green eyes. Is it unusual? (c) What is the mean and standard deviation of this distribution?