3) A popular resort hotel has 300 rooms and is usually fully booked. About 6% of the time a reservation is canceled before the 6:00pm deadline with no penalty. a. What is the probability that exactly 280 rooms will be occupied? b. What is the probability that at least 280 rooms will be occupied? c. What is the probability that all 300 rooms will be occupied? 10) Below is the number and frequency of a college baseball team's runs during the 2017 regular season. Runs 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Frequency 1 2 2 3 6 7 5 4 1 2 2 1 0 2 1 1 a. Find the empirical probabilities of 0-15 runs scored during the 2017 season. b. Assuming a Poisson distribution and using the mean number of runs per game from the empirical data, compute the probabilities of experiencing 0-15 runs in a game. Compare these theoretical probabilities to your answer in part a. c. Construct a chart to visualize your results. d. How well does a Poisson distribution model this phenomenon? Which probability would you use to predict runs for the next season