I've been working on this problem for a while, but it'd be a lot easier if I had an equation to work with.
Here's the deal; the problem is hypergeometric.
#of successes within pop=X=40
# of successes within samples=x
The question asks the probability that p-hat (of sample successes) exceeds 0.20
I just don't have the right formulas for this... I was able to get that for p-hat to equal 20, x=12.8; and I could find the probability for that specific value using the combinations formula... but the question is asking for the probability that p-hat is greater than or equal to .2, not just equal to. Also, I'm pretty sure that this is the same as the probability that x is greater than or equal to 12.8.
Any help would be much appreciated as I've hit a brick wall!