We consider the random experiment that consists of rolling two dice. Let $\mathrm{M} $ be the sum of the number of dots on the two dice. a) In a table, list all of the possible outcomes for the random variable $\mathrm{M}$ together with its distribution and cumulative probability distribution. Sketch both distributions. b) Calculate the expected value and the standard deviation for M. Interpret your results. c) Looking at the sketch of the probability distribution, you notice that it resembles a normal distribution. Should you be able to use the standard normal distribution to calculate probabilities of events? Why or why not? Discuss and explain your answer. SP.AS352