8.70% of students at a large New York University receive some financial aid. a.If 4 students are randomly selected, determine the probability that exactly 2students in the sample receive some financial aid. b.If 4 students are randomly selected, determine the probability that less than 2students in the sample receive some financial aid. . 9.Serious accidents occur at an oil refinery at a Poisson rate of 1 per year.a.Find the probability ofexactly 2serious accidents occurring in the next year. b.Find the probability of at least 1serious accident occurring in the next 3 years.10.The random variable X follows the probability distribution function as shown to the right: a.Determine P(X=3) b.Determine the population mean. c.Determine the population variance 11.39% of students at a college use the cafeteria. a.If 9 students are randomly sampled, determine the probability that less than 3 use the cafeteria. (Probability table for binomial n=9, p=.39 shown on the right) ---------------------b.If 9 students are randomly sampled and X represents the number of students in the sample who use the cafeteria, find the meanand standard deviationof X. 12.Accidents in a power plant occur at a Poisson rate of 1.39 per year a.Find the probability of at least2accidents occurring at the plant in the next year. b.Find the probability that the plant has zero accidents in two year. 13.Find the 30thpercentile for each of the following populations: a.Cooking time for oatmeal which follows a Normal Distribution with a mean of 4and a standard deviation of b.The amount of coffee in a carafe which Uniform Distribution with a minimum of 3ozand a maximum of 23oz. c.The waiting time until a plant accident which is an Exponential Distribution with a mean of 10 years.14.Students’ exam scores for a course follow a Normal Distribution with =70and =10. a.Find the probability a randomly selected student scores a 75 or moreb.Find the exam score which is the 25thpercentile of this distribution. c.You take a random sample of 40 students. Find the probability the sample meanis between 68 and 72. d.Would your answer for part c be different if the probability distribution of “exam scores” did not follow a Normal distribution? Explain your answer3 .