STAT 1040 final exam has 30 multiple choice questions with four choices (A-D) with one correct answer each. A student claims that she randomly selected answers to 30 multiple choice questions. Let X be the number of correct answers if she guesses randomly from the 4 choices for each of the 30 questions. a. What is the probability distribution of X? Find the mean and standard deviation of the random variable X. b. What's the probability that she guessed 20 questions correctly, by chance alone? c. What's the probability that she guessed more than 10 questions correctly, by chance alone?