Southern University System In https://moodle.sus.edu/pluginfile.php/787/question/qu stiontext/105075 7. (6 points) Suppose that houses in West Baton Rouge area are sold at a rate of 1.02 per day, and that on average, 13.3% of the houses sold are built in the first half of 1963 or earlier (we will call such houses "old" ). Real estate agent Sally has noticed that the numbers of houses, old and new, and the numbers of buyers and sellers in the market, are very large compared to the number of sales that typically occur in a month. Therefore she adopts the following mathematical modeling assumptions: Ages of houses sold are independent of one another, and the number of sales, and the time until the next sale, are independent across time periods. Based on these assumptions answer (a)-(d) below; for each question, state clearly what distribution it follows. a) Find the probability that exactly 1 of the next 7 houses sold will be "old". b) Find the probability that exactly 8 houses will be sold in the next (7-day) week. c) What is the probability that it will be at least a 7-day week (from now) before the next house is sold