Assume that a tire manufacturer thinks that the lifetimes of its tires follow normal distribution with mean 48,000 miles and standard deviation 5,000 miles.
1. If the manufacturer desires to issue a guarantee so that 99% of its tires last for longer than the guaranteed lifetime, what z-score should it employ to determine that guaranteed lifetime?
2. If the manufacturer wants to issue a guarantee so that 99% of its tires last for longer than the guaranteed lifetime, how many miles should it advertise as its guaranteed lifetime?