Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of75,000

miles and a standard deviation of

miles. These tires come with a55,000

-mile warranty. The manufacturer of the tires can adjust

during the production process, but the adjustment of

is quite costly. The manufacturer wants to set

once and for all so that only2

%

of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

miles