A fair four-sided die is rolled n times. Let Sn = X1 + X2 + . . . + Xn, where Xi is the number showing on the ith roll. Determine a condition on n such that the probability that the sample average Sn n is within 20% of the mean µX is greater than 0.92. (a) Solve the problem using the form of the law of large numbers based on the Chebychev inequality. (b) Solve the problem using the Gaussian approximation for Sn, which is suggested by the CLT. If you need to find Q(x) or Φ(x), round x to the nearest hundredth. (Note: Do not use the continuity correction for this question, because, unless 2.5n ± (0.2)nµX are integers, inserting the term 0.5 is not applicable).