The U-Drive car rental corporation has found that the cars in the company's rental fleet experience punctures at the rate of 1.25 punctures per 10,000 miles, and the number of punctures per distance traveled is Poisson distributed. Ed and Harriet are taking advantage of a U-Drive promotion in which there is no mileage charge. During their vacation, they plan to drive from Boston to Los Angeles and back, a total distance of 6164 miles.
a. What is the probability that Ed and Harriet will not have to change any tires during their vacation?
b. While traveling west, what is the probability that Ed and Harriet will experience a punctured tire before they make it to Denver, 2016 miles away?
c. For what mileage is the probability 0.80 that Ed and Harriet will experience a puncture before they reach this distance?