1. Multiple-Choice Test Because they are so easy to correct, multiple-choice questions are commonly used for class tests, SAT tests, MCAT tests for medical schools, and many other circumstances. The table in the margin describes the probability distribution for the number of correct responses when someone makes random guesses for 10 multiple-choice questions on an SAT test. Each question has 5 possible answers (a,

b,

c, d, e), one of which is correct. Assume that random guesses are made for each of the 10 questions.

a. Verify that the table satisfies the requirements necessary for a probability distribution.

b. Find the mean number of correct responses.

c. Find the standard deviation for the numbers of correct responses when random guesses are made for the 10 questions by many different subjects.

d. What is the probability that someone gets at least half of the questions correct?

e. When someone makes guesses for all 10 answers, what is the expected number of correct answers?

f. What is the probability of getting at least 1 answer correct?

g. If someone gets at least 1 answer correct, does that mean that this person knows something about the subject matter being tested?