1. Suppose 55% of babies born in a certain country are female. We take a random sample of 20 babies from this country. Use the Binomial table to answer the following.
a. Find the probability that exactly 15 babies are female.
b. Find the probability that no more than 12 babies are female.
c. Find the probability that at least 4 babies are female.
d. Suppose we observe that 17 of the 20 babies are female. Would you consider this an unusually high number? Calculate a probability to justify your answer.
2. As in problem, suppose 55% of babies born in a certain country are female. Now, we take a random sample of 200 babies from this country. Use the Normal approximation to the Binomial to find the probability that at least 100 babies are female.