Suppose that the lifetimes of tires of a certain brand are normally distributed

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 sigma miles. These tires come with a 65,000-mile warranty. The manufacturer of the tires can adjust sigma during the production process, but the adjustment of sigma is quite costly. The manufacturer wants to set sigma once and for all so that only 2% 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.

Explanation / Answer

P(X < 65000) = 0.02

=>

P( Z < 65000 - 75000/sigma) = 0.02

=>

65000 - 75000/sigma = invnorm(0.02)

65000 - 75000/sigma = -2.054

=>

sigma = 4868.6 ..........ans

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