This test, like many multiple-choice tests, is scored using a penalty for guessing. The test score is determined by awarding one point for each question answered correctly, deducting 0.25 points for...

This test, like many multiple-choice tests, is scored using a penalty for guessing. The test score
is determined by awarding one point for each question answered correctly, deducting 0.25 points
for each question answered incorrectly, and ignoring any question that is omitted. That is, the
the test score is calculated using the following formula

score=(1Xnumber corrected)-(0.25Xnumber incorrect)+(0 X Number omitted)

(b) Suppose a student knows the correct answers for 18 questions, answers those 18
questions correctly, and chooses randomly from the 5 choices for each of the other 7
questions. Show that the expected value of the student’s score is 18 when using the
the scoring formula above.