SOLUTION: 60. 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 m

Question 124867: 60. 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? the answer is 32.56, I just need to know how this was computed by showing the work.
Answer by stanbon(75887) (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. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer�s expense? the answer is 32.56, I just need to know how this was computed by showing the work.
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Draw a normal curve; put the mean of 36.84 at the middle; mark some
point on the horizontal axis as the point below which 10% of the population
lies.
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Find the corresponding z-value for that point: it is z=-1.2816
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Find the corresponding "x" or raw-score value:
z(x) = (x-mu)/sigma
-1.281552 = (x-36.84)/3.34
x-36 = 3.34*(-1.281552)
x = 31.72 months
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Comment It doesn't turn out to be 32.56 but it is correct if you are
using a z-distribution
But if you are supposed to use a t-distribution you would get:
t(x) = (x-36.84)/3.34
Using t = -1.282 you get:
x-36 = -1.282*3.34
x = 31.72 months
---------------------------
Both results are the same.
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Cheers,
Stan H.

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