According to data from the CDC, about 43% of adults in the United States (individuals 18 years of age or older) received a flu vaccine during the 2014-2015 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 adults.

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

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

c) State any assumptions you needed to make in order to answer parts a) and b).