the chemical company manufactures car tires that last distance having a normal d

Question

the chemical company manufactures car tires that last distance having a normal distribution with a mean of 35600 and a standard deviation of 5275 miles. draw a picture of a. What is the probability that would randomly selected tires last less than 40,000 miles? B. If the manufacturer wants to guarantee the tires so that only 8% will be replaced because of failure before they guaranteed number of miles, for how many miles should the tires be guaranteed round answer to the nearest mile. c. what a tire lasting less than 25000 miles be unusual explain

Explanation / Answer

Z for 40,000 miles

Z = (40,000-35,600)/5275 = 0.834

P(Z<z) = 0.797

For next part,

We want a z such that P(Z<z) =0.08

Z = -1.4

X = 35600 - 1.4*5275 = 28188

So Tires should be guaranteed for 28188 miles

P ( X<25000) = 0.022 {same mthod}, this means that there is only 2% chance that tires can last less than 25000. So if it happens, then it is indeed unusual.

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