Suppose that 30% of the births in the US are done by Cesarean section. 

(a) If 8 births are selected at random, what is the probability that at least two of them were Cesareans?.

(b) If 80 births occur one week in NYC, what is the probability that at least twenty of them are Cesarean? (use normal approximation) Explain why this is higher or lower than the answer in part (a).

(c) If 10 mothers give birth, what is the probability that less than two of them have Cesareans?

(d) If 100 mothers give birth, what is the probability that less than twenty of them have Cesareans? Explain why this is higher or lower than the answer in part (c).