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 flu vaccine during the 2017-2018 flu season.

a) Consider a random sample of 50 adults.

i. Calculate the probability that exactly 20 adults received a flu vaccine.

ii. Calculate the probability that exactly 30 adults did not receive a flu vaccine.

b) Consider a random sample of 20 children.

i. What is the probability that at most 10 children received a flu vaccine?

ii. What is the probability that at least 11 children received a flu vaccine?

c) State two assumptions you needed to make in order to answer parts a) and b). Briefly comment 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 children. Let Z represent the total number of individuals who received the flu vaccine in the sample of 70 individuals. Does Z follow a binomial distribution? Explain your answer.