# Poisson / hypergeometric distribution help please?

• Oct 2nd 2009, 07:09 AM
Intsecxtanx
Poisson / hypergeometric distribution help please?
About one in 28 Americans 40 and over, are blind or have vision so poor that even with glasses, medicine or surgery, everyday tasks are difficult, according to the National Eye Institute, a federal agency. Let X be the number of blind Americans in a sample of n = 60.
1. How is X distributed?
2. Find the probability that X is at least 3.
3. Find the probability that X is at most 3.
4. Find the probability that X is equal to 3.

I'm so lost as to which distribution to use and how to calculate these probabilities. any help will be appreciated thank you.(Bow)
• Oct 2nd 2009, 07:48 AM
galactus
Are you familiar with binomial probability?.

At least 3: $\sum_{k=3}^{60}\binom{60}{k}(\frac{1}{28})^{k}(\fr ac{27}{28})^{60-k}$

or equivalently:

$1-\sum_{k=0}^{2}\binom{60}{k}(\frac{1}{28})^{k}(\fra c{27}{28})^{60-k}$

The latter will probably be easier to calculate, unless you use a calculator.