Professor Kate likes to exclusively buy boxes of cereal with prizes inside. However, she has found that in fact only about 90% of the boxes of cereal that she’s bought in the past have prizes in them. If Professor Kate lives off of cereal and buys 50 boxes of cereal over the next year, (a) find the probability that she will collect more than 47 prizes. (b) Approximate the probability you found in part (a) with a Poisson distribution. Do not leave your answer in an infinite sum. (c) Is using a Poisson distribution for an approximation a good choice in this case? Explain your answer in a few brief sentences