A mechanic sells a brand of automobile tire that has a life expectancy that is n

Question

A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 28,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires? Click to view page 1 of the tabl Tires that weo by miles will be replaced free of charge. e. Click to view page 2 of the table. (Round to the nearest mile as needed.)

Explanation / Answer

Mean = 28000

Sd = 2500

P(X < x) = 0.1

Or, P(Z < (x - 28000)/2500) )= 0.1

Or, (x - 28000) / 2500 = - 1.28

Or, x = 28000 - 1.28 * 2500

Or, x = 24800

Tires that wear out by 24800 miles will be replaced free of charge

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