Hyundai advertises a 10 year-100,000 mile power-train warranty for its cars. You

Question

    Hyundai advertises a 10 year-100,000 mile power-train warranty for its cars.  You work for a competitor and want to see if you can meet this for your vehicles.  You have collected engine performance data and determined that the life is approximately normally distributed with a mean of 112,300 miles and a standard deviation of 4800 miles.  (a.) What percentage of the engines will fail by 100,000 miles?  (b.) At what mileage should you set the warranty for your vehicles if you are willing to repair 1% at no cost to the consumer?

Explanation / Answer

using X=m+Z*s , m is mean, s is standard deviation

a) X= 100000 => Z = -2.5625

From the standard distribution curve, 0.6 % cars will fail (refer to any distribution table)

b) From the table, Z= -2.3 => x= 101260

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