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 29,000 miles and a standard deviation of 2200 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 table. Click to view page 2 of the table. Tires that wear out by miles will be replaced free of charge Round to the nearest mile as needed.)

Explanation / Answer

Mean is 29000 and s is 2200

for bottom 10% we need to see the z for 90% and negate it. thus, from normal distribution table we get -1.28

therefore answer is mean+z*s=29000-1.28*2200=26184

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