A tire company finds the lifespan for one brand of its tires is normally distrib

Question

 A tire company finds the lifespan for one brand of its tires is normally distributed with a mean of 47,500 miles and a standard deviation of 3000. If the manufacturer is willing to replace no more than 10% of the tires, what should be the approximate number of miles for a warranty?   

Explanation / Answer

Let m be the approximate minimum or cut-off number of miles thatthe manufacturer should set for a warranty of the tires. P(x>m) =10% P{x>[(m-47500)/3000]} =0.10 So, [(m-47500)/3000] = Z0.10 [(m-47500)/3000] = Z(0.5-0.4) i.e., [(m-47500)/3000] = 1.28 m-47500 = 1.28 * 3000 m-47500 = 3840 m = 51340 Therefore, the manufacturer should set the minimum or cut-offnumber of miles to be approximately 51340 for a warranty of thetires, if he/she is not willing to replace no more than 10% of thetires.

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