An educational consulting firm is trying to decide whether high school student who have never before used handheld calculators can solve a certain type of problem more easily with a calculator that uses reverse Polish logic or one that does not use this logic. A sample of 25 student is selected and allowed to practice on both calculators. Then each student is asked to work one problem on the reverse Polish calculator and a similar problem on the other. Let p = P(S), where S indicates that a student worked the problem more quickly using revers Polish logic than without, and let X = number of S’s. a) If p = 0.5, what is P(7 ≤ X ≤ 18)? b) If p = 0.8, what is P(7 ≤ X ≤ 18)? c) If the claim that p = 0.5 is to be rejected when either X ≤ 7 or X ≥ 18, what is the probability of rejecting the claim when it is actually correct? d) If the decision to reject the claim p = 0.5 is made as in part c), what is the probability that t