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NeverFail manufacturing produces very expensive hard disks for personal computers. The disks have a mean life of 10,000 days with a standard deviation of 370 days. NeverFail wants to advertise a guaranteed life, in days since purchase, and to offer free replacement if a disk drive fails earlier than the 10,000 days. What should the guaranteed life be if they want the chance of having to replace the drive to be less than 1 in 200? We can determine from the z table that a standard score of 2.58 from the mean will cut off a tail area of 0.5% of the total area under the curve. There will be two such ordinates, cutting off lower and upper tails, at L and M. Drives with lifetimes to the left of L will fail the guarantee. L is a distance of 10,000 - (2.58 s.d. x 370) = 9045.4. Thus the chance of a drive having a life of 9045.4 days or less is just .5%. Playing it safe the guarantee is set at 9000 hours.
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