1. (15 pts) Statistics released by the National Highway Traffic Safety Administration and the National Safety Council show that on an average weekend night, 1 out of every 10 drivers on the road is drunk and it is known that this data is normally distributed. If 400 drivers are randomly checked next Saturday night, what is the probability that the number of drunk drivers will be a. (5 pts) Less than 32? b. (5 pts) More than 49? c. (5 pts) At least 35 but less than 47? 2. (10 pts) The lifespan of a car battery averages five years. Suppose the battery lifespan follows an exponential distribution. a. (3 pts) Find the probability that a randomly selected car battery will last more than three years. b. (3 pts) Find the variance of the battery lifespan. . (4 pts) Suppose a three-year-old battery is still going strong. i. Find the probability the battery will last an additional five years. 11. How much longer is this battery expected to last