Question 175302: In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
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Draw a normal curve with mean 36.84.
Sketch a left tail containing 10% of the population of HDTV that fail.
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Find the z-value corresponding to left-tail 10%: -1.2816
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Find the x-value corresponding to that z-value:
z(x) = (x-u)/sigma
-1.2816 = (x-36.84)/3.34
x-36.84 = -4,2804
x = 32.56 months is the upper limit of time for the warranty.
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Cheers,
Stan H.
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