Assume that the number of miles a particular brand of tire lasts before it needs to be replaced follows a normal distribution with a mean of 45,600 miles and a standard deviation of 5,800 miles.
a. What is the probability that the next tire of this brand sold will last
1. More than 36,000 miles before it needs to be replaced?
2. Less than 42,000 miles before it needs to be replaced?
3. Between 45,000 and 55,000 miles before it needs to be replaced?
b. Use Excel or PHStat to confirm the answers in part a.
c. What is the mileage that 90% of the tires of this brand will survive before needing to be replaced?