8. A superball machine ejects balls with numbers in the set {1,2,3,..20}. Determine the distribution, parameter(s), and support for each scenario below, and answer the probability question asked. Assume there are only 20 balls in the machine, each of which is unique. a) If we sample 25 balls from the machine by recording the value of each ball and placing it back in the machine each time, determine the probability that exactly 5 of the have a value greater than 10. b) If we sample 14 balls from the machine but do not replace them, determine the probability that the sample contains exactly 5 balls with a value greater than 10. c) If we sample with replacement, determine the probability that the value of the 6th ball is the first with a value greater than 10. d) The machine has been configured to automatically eject a ball and then replace it with a ball of the same number. The machine runs constantly and sporadically ejects a ball. This happens on average every 5 minutes. A ball was just ejected, determine the probability that it takes more than 7 minutes before the next ball is ejected. e) The machine is running in automatic mode as in part d). A ball was just ejected, determine the probability that the next ball ejected has a value greater than 10. f) The machine is running in automatic mode as in part d). But, has been reconfigured to sample a ball uniformly at random with a time between 4 minutes and 8 minutes, determine the 68th percentile of the time between each sample. 8. A superball machine ejects balls with numbers in the set {1,2,3,..20}. Determine the distribution, parameter(s), and support for each scenario below, and answer the probability question asked. Assume there are only 20 balls in the machine, each of which is unique. a) If we sample 25 balls from the machine by recording the value of each ball and placing it back in the machine each time, determine the probability that exactly 5 of the have a value greater than 10. b) If we sample 14 balls from the machine but do not replace them, determine the probability that the sample contains exactly 5 balls with a value greater than 10. c) If we sample with replacement, determine the probability that the value of the 6th ball is the first with a value greater than 10. d) The machine has been configured to automatically eject a ball and then replace it with a ball of the same number. The machine runs constantly and sporadically ejects a ball. This happens on average every 5 minutes. A ball was just ejected, determine the probability that it takes more than 7 minutes before the next ball is ejected. e) The machine is running in automatic mode as in part d). A ball was just ejected, determine the probability that the next ball ejected has a value greater than 10. f) The machine is running in automatic mode as in part d). But, has been reconfigured to sample a ball uniformly at random with a time between 4 minutes and 8 minutes, determine the 68th percentile of the time between each sample