a multiple choice exam consists of 24 questions, each with 4 possible answers, of which only one is correct. A student chooses an answer at random for each question. Let X be the number of correct answers.

a) find the expected value and variance of X.

b) find the probability that the student gets all the answers correct.

c) use the normal approximation to the binomial to find the probability that the student gets at least 12 answers correct.