Klinefelter syndrome, alternatively known as XXY, is a genetic disorder characterised by the presence of an extra X chromosome. The disorder only affects males. Suppose a researcher estimates that the probability that a newborn male will have Klinefelter syndrome is . Suppose that a particular hospital delivers male babies in a year.

Part a) Using a binomial model, what is the probability that more than two of the male births have Klinefelter syndrome? Give your answer to four decimal places.


Part b) An approximation to the above probability can be found using a Poisson distribution. Find the Poisson approximation to the probability you gave in (a), giving your answer to four decimal places.


Part c) Taking the binomial probability as the base (that is, 100%), by what percentage does the Poisson approximation differ from the binomial probability? Please use the rounded (four decimal places) probabilities in your calculation and give your answer as a positive value to three decimal places.