Past insurance company audits have found that 2 percent of dependents claimed on an employee's health insurance actually are ineligible for health benefits. An auditor examines a random sample of 8 claimed dependents. (a) What is the probability that all are eligible? (Round your answer to 4 decimal places.) Probability (b) What is the probability that at least one is ineligible? (Round your answer to 4 decimal places.) Probability Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,986 pounds to 4,104 pounds. (a) What is the mean weight of a randomly chosen vehicle? (Round your answer to the nearest whole number.) Mean weight (b) What is the standard deviation of a randomly chosen vehicle? (Round your answer to 4 decimal places.) Standard deviation (c) What is the probability that a vehicle will weigh less than 3,089 pounds? (Round your answer to 4 decimal places.) Less than 3,089 pounds (d) What is the probability that a vehicle will weigh more than 4,075 pounds? (Round your answer to 4 decimal places.) More than 4,075 pounds (e) What is the probability that a vehicle will weigh between 3,089 and 4,075 pounds? (Round your answer to 4 decimal places.) Between 3,089 and 4,075 pounds Answer the following: (a) At what x value does f(x) reach a maximum for a normal distribution N(85, 3)? Maximum height (b) Does f(x) touch the X-axis at 30? Yes No