A multiple choice test has 25 questions each with 5 options. 4 points are given for each correct answer and 1 point is subtracted for each incorrect answer. Homer and Lisa are among a large number of test takers.
a) Homer guesses randomly on all 25 questions. What is the chance he gets at most 2 correct?
b) Homer's possible scores ranges from ...to...?
c) What is the expected value and SE of his score?
d) The chance that Homer gets 9 or more questions correct is approximately?
e) Lisa knows the answer to 21 questionsand randomly guesses on the remaining for questions. Her possible total score ranges from .... to.....?
f) The chance that the Lisa gets her lowest possible score is?
g) Lisa's expected score?
h) The SE of Lisa's score?
i) There were many other test takers like Homer who randomly guessed on all 25 questions. A scatter plot for all of them showing the number of correct answers vs. the number of incorrect answers has a correlation of ?