Suppose that you own a company that sells tires for automobiles. The lifespan of

Question

Suppose that you own a company that sells tires for automobiles. The lifespan of your tires gives a normal distribution. The mean life of a tire is 35,000 miles and the standard deviation is 3,000 miles. You want to offer a warranty to your customers to replace tires that don't last very long. Suppose you are willing to replace 10% of the tires. What mileage should you include in your warranty? Round your answer to the nearest mile. In other words, complete this sentence: A refund will be given on all tires that last less than _______ miles.

Explanation / Answer

here as we know that for bottom 10 percentile ; critical z =-1.2816

therefore corresponding warranty life =mean +z*std deviation =35000 -1.2816*3000=31155 miles

refund will be given on all tires that last less than 31155 miles.

( please try 31160 if above does not works due to rounding error in z score)

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