Re: Need some hints for a probability problem

I am looking at solving the following problem:

Problem: Suppose the current median age of U.S. citizens is 30. If a
survey of 500 randomly slected U.S. citizens is conducted, what is the
probability at most 240 of them will be under 30 years old.

Should this be modeled as a hypergeometric distribution, and if so,
how do I go about it? Any help would be great!

Thanks!


The number of successes "a sample being less than 30" is modeled with a binomial distribution. The problem tells you the probability of success Pr(x<30)=.5. The mean of the binomial is 500*.5 = 250 and the variance is 500(.5)(.5)=125. You can use the mean and variance to figure out how many standard deviations away from 250 240 is and use a normal approximation to calculate Pr(x<240)
.