Problem 1. According to data from the CDC, about 37.1% of adults (individuals 18 years of age or older) in the United States and 57.9% of children (individuals between 6 months and 17 years of age) in the United States received a u vaccine during the 2017-2018 u season. For any calculations, be sure to demonstrate the reasoning behind your calculations, such as by dening the relevant random variable(s), using probability notation, and/or briey writing out your thought process. a) Consider a random sample of 50 adults from the Boston area. i. Calculate the probability that exactly 20 adults received a u vaccine. ii. Calculate the probability that exactly 30 adults did not receive a u vaccine. b) Consider a random sample of 20 children from the Boston area. i. What is the probability that at most 10 children received a u vaccine? ii. What is the probability that at least 11 children received a u vaccine? c) State two assumptions you needed to make in order to answer parts a) and b). Briey com- ment on the extent to which those assumptions were reasonable. d) Consider a random sample of n = 70 individuals, which consists of 50 adults and 20 chil- dren. Let Z represent the total number of individuals who received the u vaccine in the sample of 70 individuals. Does Z follow a binomial distribution? Explain your