Let X denote the score of an exam and suppose follows a normal distribution with mean 50 and standard deviation 3. Suppose of a big group of students took this exam. (a) What is the 25th percentile of their score? You may use the fact that the 25th percentile of a standard normal random variable, Z is -0.674. (b) What is the percentage of students whose scores are between 47 and 59? Note that for a standard normal random variable Z, Φ(3) = P(Z ≤ 3) = 0.999 and Φ(1) = P(Z ≤ 1) = 0.841. (c) What is E(X2 )?