text: can anyone help with a statistics problem? an instructor is planning on giving a multiple choice test. recognizing that students may use a guessing strategy, she wants to deduct points for providing the wrong answer. the test will consist of 25 problems, each with 5 choices. the instructor will award 4 points for a correct answer, but wants the expected value of the grade to be 0 for a student who gueses. how would the penalty work?  what if the test consisted of 20 problems with 4 choices each? 5 points for a correct answer. what is the penalty?   what if the test had 30 problems with 3 choices each? 3 and 1/3 points for a correct answer. what's the penalty?  what if the test had 50 true/false type problems. 2 choices and 2 points for each correct answer. what's the penalty?   **if anyone can help to solve this problem, please tell me if there's some formula you have to use to solve it. i have a statistics book, but have no idea which formula, if any, i should use to solve it. thanks!!!** first one:  25 * [1/5 (4) + 4/5 (x)] = 0 20 + 20x=0 20x = -20 x = -1  second one: 20 [1/4 (5) + 3/4 (x) ] = 0 25 + 15x = 0 15x = -25 x = -25/15 x = -1 2/3  third one: 30 [ 1/3 (3 1/3) + 2/3 (x )] = 0 100/3 +20x = 0 20x = -33 1/3 x = -1 2/3  50 [ 1/2 (2) + 1/2 (x) ] = 0 50 + 50x = 0 50x = -50 x = -1