SOLUTION: 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

Question 135433: 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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To help you see what is happening here:
1st: Sketch a normal curve over a z-axis.
2nd: Put a nick on the horizontal axis where you expect only 10% of the
population lay.
The z-value of that point is z=1.282
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3rd: Mark the middle (mean) value that axis.
The z-value there is 0.
------------------------------------
Your problem:
4th Find the raw score (x) value that corresponds to z=1.645 using
z = (x-mu)/sigma
1.282 = (x-36.84)/3.34
x-36.84 = 1.282*3.34
x = 41.12 months
The warranty should be set at appoximately 41 months.
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Cheers,
Stan H.

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