In a National Highway Traffic Safety Administration report, data provided to the NHTSA by Goodyear stated that the average tread life of property inflated automobile tires is 45,000 miles. Suppose that the current distribution of tread life of properly inflated automobile tires is normally distributed with a mean with a mean of 45,000 mies and a standard deviation of 2360 miles.
a.) Suppose that 6% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.
b.) Suppose that 2% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.