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1. (20 points) Your professor likes to exclusively buy boxes of cereal with prizes inside. She has three favourite cereal brands: Cheerios, Frosted Flakes and Kellogg's. However, she has found that in fact only about 90% of Cheerios, 85% of Frosted Flakes, 75% of Kellogg's that she's bought in the past have prizes in them. According to the avors, she bought Cheerios, Frosted Flakes and Kellogg's with probability 0.5, 0.3, 0.2 respectively. If your professor lives off of cereal and buys 50 boxes of cereal over the next year, (You don't need to simplify your answer.) (a) nd 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 innite sum.) (c) Is using a Poisson distribution for an approximation a good choice in this case? Explain your answer in a few brief sentences. (d) Approximate the probability you found in (a) with a normal distribution.(Leave your answer with @) (e) Is using a Normal distribution for an approximation a good choice in this case? Explain your answer in a few brief sentences