Question

Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74,000 miles and a standard deviation of o miles. These tires come with a 55,000-mile warranty. The manufacturer of the tires can adjust o during the production process, but the adjustment of o is quite costly. The manufacturer wants to set o once and for all so that only 1% 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 5 ?

Answer 1

Solutions Given that the lifetimes a certain brand are normally distributed with mean of 74000 miles and Standard deviation 6 miles. of tires te Let x = life times of tires Then, Xon N( 74000, 62) Allo the warranty te Delf je 55oou mile. We have to fina do that only 1% of the tiges will fail before warranty expiges. til P ( x <S5ooo) oool => P(x-u < il soooru) 4ove) =) Pl za Cooss 740 = 001 > z lda 19000) - 0.01 くこ - 1 gous o Zoio EDCE.C- (from stanood normal table)

То) до - 2, 32 63 с (— 6. – 19 о. 9. 32 G2 8) 64 .41 63 а) о 31 Sa. S С», the Itanaara deviation о be let such that only faid before warranty 1. of the tiree بدن با St) ( 8 т о кә