A multiple-choice test has nine questions. For each question there are four possible answers from which to select. One point is awarded for each correct answer, and points are not subtracted for incorrect answers.
The instructor awards a bonus point if the students spell their name correctly. A student who has not studied for this test decides to choose an answer for each question at random.
a. Find the expected number of correct answers for the student on these nine questions.
b. Find the standard deviation of the number of correct answers for the student on these nine questions.
c. The student spells his name correctly:
i Find the expected total score on the test for this student.
ii Find the standard deviation of his total score on the test.