One hundred Lower Wabash Tech students take the 10-question multiple-choice test with 4 answers to each question, exactly one of which is correct. All of students are unprepared and should guess at each question.
1. How many unprepared students would've to take this test to guarantee ten score of 6? Ten scores of 7? Ten scores of 8? Show your work or explain your reasoning.
2. Sarah as well takes the test, and she wants to know how many correct answers she and Richard can expect to get all together. Answer Sarah's question.
3. Find out the standard deviation of the difference between Sarah's and Richard's scores?
4. Richard wants to know how many questions he will have to answer till he gets one correct. Has the random variable changed (i.e., is it now different from the one you identified in (a)?)? If so, recognize this new random variable and justify your answer. Then answer Richard's question.