The lifetimes (in miles) of a certain brand of automobile tires is a normally distributed random variable, X, with a mean lifetime of =40,000 miles and standard deviation =2000 miles.

• The manufacturer would like to offer a guarantee for free replacement of any tire that does not last a specified minimum number of miles. If the manufacturer desires to have a replacement policy that they will need to honor for only 1% of all tires they sell, what number of miles should be included in the following guarantee: We will replace any tire free of charge if the lifetime of the tire is less than _________________miles. (That is, what is the largest value for a lifetime a tire can have and still be among the shortest 1% of all tires lifetimes?)