Q1) One hundred Lower Wabash Tech students take 10-question multiple-choice test with four answers to each question, exactly one of which is right. All of students are unprepared and should guess at each question.   

i) How many unprepared students would have to take this test to assure ten score of 6? Ten scores of 7? Ten scores of 8? Illustrate your work or describe your reasoning.

ii) Sarah also takes test, and she wishes to know how many right answers she and Richard can expect to get all together. Answer Sarah's question.

iii) Determine the standard deviation of difference between Sarah's and Richard's scores?

iv) Richard wishes to know how many questions he will have to answer until he gets one correct. Has random variable changed (i.e., is it now different from one you identified in (a)?)? If so, recognize this new random variable and give explanation for your answer. Then answer Richard's question.