Question 124867
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
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Both results are the same.
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Cheers,
Stan H.