5. Given the Distribution: X 1 3 4 5 P(X] .05 0.3 0.35 ? 0.10 Find P(X = 4), and u. 6. Approximately 80% of all the U.S. chief executive officers (CEOs) have a college degree. In a group of 13 CEOs, what is the probability that exactly 9 have college degrees? 7. It has been estimated that only about 30% of California residents have adequate earthquake supplies. Supplies we are interested in the number of California residents we must survey' until we find a resident who does NOT have adequate earthquake supplies. a. What is the probability that we must survey just 1 or 2 residents until we find a California resident who does not have adequate earthquake supplies? b. How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies? 8. An unprincipled used car dealer sells a car to an unsuspecting buyer, even though the dealer knows that the car will have a major breakdown, anytime within the next 6 months. The dealer allows a warranty of 45 days on all cars sold. Let x represent variable with values between 0 and 6 months. a. Find the probability that the breakdown occurs while the car is still under warranty. b. Calculate the 55th percentile. c. Calculate the mean. 9. Given X ~ B(33,0.4), find the mean and standard deviation. 25