8. Let :r represent the number of lease agreements a car saleswoman makes per month. I is a discrete random variable with the following distribution: I Number of Leases, I 0 1 2 I Probability, P[I) 0'4 0'5 0'1 (21) Find #4,, the expected number of lease agreements she makes per month (b) Find a, (c) The number of cars she sells per month, 11, is a random variable with mean W = 1.1 and standard deviation (7y = 0.9. Suppose that she gets a $300 bonus for each car (3:) she leases and $500 for each car she sells. Let the random variable 7' represent the total monthly bonus she earns Write an equation for 7', and nd or and HT. 9. 8% of US residents have blue eyes. Suppose that US residents are selected at random from the population (with replacement) until one with blue eyes is chosen. (a) What is the probability that the fourth person selected is the rst one with blue eyes? (b) What is the probability that it takes 2 or more selections until selecting the rst person with blue eyes? 10' A severe tornado occurs in Lubbock, Texas (on average) 2 times every 50 years. (a) What is the probability that Lubbock has five severe tornadoes in next 75 years? (b) What is the probability that Lubbock has at least two severe tornadoes in the next 30 years? Bonus. What is the probability that Lubbock has at lcast one tornado in the next 8 100 years, given that there are less than four tornadoes in the next 100 years