You are to roll a fair die n 113 times, each time observing if the topside of the die shows a 6 (success) or not (failure). After ob- serving the n = 113 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 • ? ⚫is approximately Normal is exactly Normal ⚫ is Binomial ⚫ is Uniform ⚫is Hypergeometric ⚫ is Poisson . with a mean and a standard deviation Enter your answer using all the decimals you can. (b) Now think about the proportion of your n = 113 tosses that show a six. What can you say about the distribution of this pro- portion? Complete the sentence, Enter your answer using all the decimals you can. The distribution of p • ? ⚫ is approximately Normal is exactly Normal is skewed to the right ⚫ is Uniform ⚫ has an unknown shape ⚫ is Binomial ⚫ is Poisson with a mean μp= and a standard deviation σ = (e) What is the probability that the proportion/percentage of your n = 113 tosses that show a six will be somewhere between 13% and 21%? Enter your answer using all the decimals you can. (d) After the n = 113 tosses of the die, you observe X = 25, the value of the sample proportion is then p=0.2212. What is the probability of observing a sample proportion that is at least this much should you decide to roll this die again 113 times? En- ter your answer using all the decimals you can.