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