Vera wants to buy 20 copies of the DVD of "Bridget Jones' Diary" as a graduation gift for the women in her sorority. She buys them from a large internet company with 50,000 of the DVDs in stock. However 10,000 of the DVDs labeled as "Bridget Jones" were really "Terminator" and just mislabeled, leaving only 40,000 correctly labeled DVDs.
a. Explain in words what X is in terms of this story. What values can it take?
b. Why is this a Hypergeometric situation? What are the parameters?
c. What are the expected number of movies she receives which are truly "Bridget Jones"?
d. What is the probability that 18 of the DVDs she purchases are actually "Bridget Jones" and not "Terminator"? Just set up the equation, but don't try to solve it.
e. What would be a good approximation to use in this situation? What are the parameters?
f. What is the approximate probability that 18 of the DVDs she purchases are actually "Bridget Jones" and not "Terminator"? Set up the equation and solve.