Suppose that the lifetimes of tires of a certain brand are n

Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of miles and a standard deviation of miles. These tires come with a -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 only 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.

Solution

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = (SEmean1^2 + SEmean2^2)

SEm = SD/(n-1)(To make things simpler, you could use n.)

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like \"areas under normal distribution\" to find the proportion/probability related to that Z score.