Question 164665: 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 themathprof(21)   (Show Source):
You can put this solution on YOUR website! For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months.
Since the mean is 36.84 then 50% will need repair before 36.84 months. So he must set the warranty to expire in less than 36.84 months. How much less? Enough so than the z-score (which will be negative) cuts off 10% of the area on the tail end on the left.
That means that the central area/percent will be 40% or .4000
This corresponds to a z-score of -1.28
Change the z=-1.28 to an x
Multiply by the s.d. and add the mean
x=zs+m
x=(-1.28)(3.34)+36.84
x=32.5648
x=32.56 months
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