Ralphie is taking a ten-question multiple choice test. each question has five choices. if ralphie answers a question correctly, he earns one point; if he answers incorrectly, he loses half a point. ralphie answers the first six questions correctly, then guesses on the last four. what is the expected value of his test score? round the answer to the nearest whole percent.
a. 52%
b. 60%
c. 68%
d. 80%

We are asked to determine the expected value of the test score given that the correct answer will earn 1 point and the wrong answer loses a half point. Initially. Raphie has answered six questions correctly so it is automatically a 60% of the test score but we need to subtract the half point deduction is 4 questions which are incorrect which has an average of -0.2. The solution is shown below:
Test Score = (6 - (4*0.2)) / 10 questions
Test Score = (6 - 0.8 ) / 10
Test Score = 0.52

The answer is 52% which is letter "A".