Problem 4. (1 point) You are to roll a fair die n = 105 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 rep- resented by Xi, i = 1,2, ... , 105. (a) Consider the distribution of the random variable X;. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die. HXi Enter your answer using all the decimals you can. Oxi Enter your answer using all the decimals you can. (b) Now think about the average of your n = 105 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 X . is approximately Normal . is exactly Normal is skewed to the right . is Uniform . has an unknown shape with a mean #x = - and a standard deviation Ox = - (c) What is the probability that the average topside on your n = 105 tosses will be somewhere between 3.3 and 3.7? Enter your answer using all the decimals you can