A class has n = 250 students, each either brings an umbrella to class or doesn't. Let us model the number of umbrellas brought to class as a Binomial Distribution with n = 250 and p = .15 137/365 .4 (see footnote2 for assumptions). i Using the model, what is the probability that exactly two umbrellas are brought to class? ii Using the model, compute the probability that 1 or more umbrellas are brought to class. iii Identify the Binomial Model assumption which is most problematic in this umbrella context (No model is perfect, but this one has an egregious problem!). Clearly state this assumption, and why your experience with umbrellas / rain disagrees with it in one or two short, clear sentences. iv (+2 pts extra credit): Given the assumption problem you identify immediately above, tell if part ii overestimates or underestimates the probability that no umbrellas are brought to class. Give a short, clear justification