The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of three birth defects per 100 births considered a typical rate in the United States.

(a) What is the probability a county that had 50 independent births during the year would have more than twice as many birth defects as expected?

(b) What is the probability a county that had 150 births during the year would have more than twice as many birth defects as expected?

(c) If you treated the number of birth defects as a Poisson random variable with mean given by .03* number of births, would you get similar answers for parts (a) and (b)?