a. Most graduate schools of Computer Science require applicants for admission to take an entry examination. Scores on one such entry exams are normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual (randomly selected) scoring above 500 in this entry exam? Also sketch the problem on a normal and standard normal distribution graph. b. The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. Prove that 99.7% fall within three standard deviations from the mean