5. Several recent studies have shown that roughly one in every 95 meteoroids entering the Earth's atmosphere is alien matter from outside our solar system. (a) Of the next 250 meteoroids entering the Earth's atmosphere, how many would you expect to be alien matter from outside our solar system? (b) Calculate the probability that, of the next 250 meteoroids entering the Earth's atmosphere, two or three meteoroids are alien matter from outside our solar system. (c) Calculate the probability that, of the next 250 meteoroids entering the Earth's atmosphere, at least two meteoroids are alien matter from outside our solar system. 6. After graphing a frequency histogram of all finishing times, the times of the finishers in a 10 km run are roughly normally distributed with mean 58 minutes and standard deviation 10 minutes. (a) Obtain and interpret the three quartiles for the finishing times. (b) What percentage of runners finished the run in less than an hour? (c) What percentage of finish times is more than two standard deviations away from the mean? (d) If two finishers are independently selected, what is the probability that for both of them it took more than an hour to finish the run? (e) In this run, sixteen Dutchmen participated and they all finished (naturally). Find the probability that a Dutchman had a finishing time between 56 and 65 minutes. (f) Calculate the probability that the average finishing time for the sixteen Dutchmen was between 56 and 65 minutes