(1 point) You are to roll a fair die n = 101 times, each time observing the number of dots appearing on the topside of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i = 1, 2, , 101. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. \"X.- = 3.5 555 Enter your answer using all the decimals you can. x]. 1.707825 EEE Enter your answer using all the decimals you can. (b) Now think about the average of your n = 101 tosses of the fair die. What can you say about the distribution of this average? Complete the sentence, Enter your answer using all the decimals you can. The distribution of )7 is approximately Normal v with a mean u)? = 3.5 ::: and a standard deviation 0')? = 015993493: ::: (c) What is the probability that the average topside on your n = 101 tosses will be somewhere between 3.3 and 3.8? Enter your answer using all the decimals you can. 0.42675 555 (d) What is the probability that the average of your in = 101 tosses is greater than 4.15? Enter your answer using all the decimals you can. 0.35197 55