You are to roll a fair die n = 108 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After observing the n = 108 tosses. you are to count the number of times the topside showed a 6. This count is represented by the random variable X. (a) The distribution of X ? c . with a mean E and a standard deviation Enter your answer using all the decimals you can. (b) Now think about the proportion of your 11 = 108 tosses that show a six. What can you say about the distribution of this proportion? Complete the sentence, Enter your answer using all the decimals you can. The distribution of if ? c with a mean up = E and a standard deviation of: l (c) What is the probability that the proportion/percentage of your n = 108 tosses that show a six will be somewhere between 13% and 22%? Enter your answer using all the decimals you can. i (d) After the n = 108 tosses of the die, you observe X = 24, the value of the sample proportion is then 5 = % = 0.2222. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 108 times? Enter your answer using all the decimals you can