Using Chebyshev and other inequality formulas (maybe even Central Limit Theorem)

[twinkiesYUM]

34.

Turner's syndrome is a rare chromosomal disorder in which girls have only one X chromosome. It affects about 1 in 2000 girls in the United States. About 1 in 10 girls with Turner's syndrome also suffer from an abnormal narrowing of the aorta.

a. In a group of 4000 girls, what is the probability that there are 0,1,2, or at least 3 girls affected with Turner's syndrome?

b. In a group of 170 girls affected with Turner's syndrome, what is the probability that at least 20 of them suffer from an abnormal narrowing of the aorta?

 

[mathman]

For both questions the most direct approach would be using the binomial distribution, although for (b.) a normal approximation would make calculation easier.

 

[awkward]

For a., a Poisson distribution is also appropriate (and probably easier to work with than the Binomial), since the probability of the disorder is so low.