The manufacturer has stated in his investigations, that the service life of a car tire is distributed approximately normally with an average of 25,000 km and a standard deviation of 2,500 km.

1. What is the probability that the lifetime of a randomly selected tire is less than 20000 km?
2. Jack randomly selects four tires for his car. What is the probability that exactly one of them does not last 20,000km?
3. What is the probability that all of them will last 20,000 km?
4. By changing the rubber compound mixture, the plant managed to reduce the likelihood that: the tire life is less than 20,000 km, to 0.015. What is the average life of a retreaded tire, assuming the reform changed the mean but not the standard deviation?
5. What is the standard deviation of the life of a retreaded tire, assuming the retread changed standard deviation but not the mean?