Professor Smith wishes to compare the performance of students in her class on multiple-choice and fill-in-the-blank exams. She randomly chooses half the class for each test. If each test has a standard deviation of 10, what is the probability of detecting a true difference ?of 5 points with a two tailed test, .05, when the sample size is (a) 10? (b) 25? (c) 50? (d) 100?