Historical Proportion

Question

A) If you want to be admitted to Big Buck U, you have to have a SAT score in the top 2% of students who take the exam. If the mean for all SAT scores is 1600 and standard deviation=120, what is the minimum score do you need?

B)If Z is a standard normal random variable find P (-.64 <= z <=0)

C) Duff Beer Company promises precisely 12 os of beer per can. If a sample can reveals a sample mean of 12.2 ounces & standard deviation 

of 0.5oz. using a level of confidence of 97%, are the cans filled correctly?

D)Ferrari drivers get lots of speeding tickets. A sample 16 of drivers is taken which determines that x bar=18 per year with s=12. Using a 98% confidence interval, what is the fewest a Ferrari driver could expect?

E) If the mean of DCCC student is 2.65 with a standard deviation of 0.4, what percentile would 2.5 put you in? 

Question

How do you recognize a situation where you need to use a two-sample test? Give a unique example of a two sample test for proportion or mean. Make sure to detail why only a two sample test would suffice.