Question

(1 point) 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 0.0014. Suppose that a particular hospital delivers 1797 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.

Answer 1

solution: X~ Bin (1997, the ARVU very large very small. n= ay 0.0014) Probability that more than 2 of mare births have Klinefelten syndrome POXY2) = 1- P(XLR) 1994- = |- Ž (1494) 6901-17 7150 004603258 0.4603 by y~ Poisson cal i n-> Assumption ngais pis ltat D Here both ne p=0.0014 & p satisfy the assump тр = 2.5158 (finite) that more than 2 of the maled births have Klinefelter syndrome PL 872) PC 922-) = 1- 2² 2.5158 (2-5158)* y=0 TY O04GOQ万34 0.4602 differ from binomial probability 8.4608-02 0.4604x100 TO0021725 N OOOQQ a Probability = 1 - e Percentage 0.4603 AN