SOLUTION: In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense.For a new HDTV the mean number of months unti

Question 164688This question is from textbook Statistcal techniques in business and economics
: In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense.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?

This question is from textbook Statistcal techniques in business and economics

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
you want to find the area under the curve of the normal distribution where 10% of the failures lie before and 90% of the failures lie after.
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that point is at 32.55962 months.
a warranty that stops there will require you to service 10% of the tv's that are sold.
90% of the tv's that are sold will experience a failure after that number of months.
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you can see this in operation by going to the following url:
http://onlinestatbook.com/java/normalshade.html
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once you get there, you put in the mean of 36.84 and the standard deviation of 3.34
you then set your shaded area to be at .1 and you select below:
it should tell you that below 32.5596 is the number you are looking for.
the shaded area under the curve represents 10% of the failures that are expected to occur and this occurs before 32.5596 months have passed.
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if you set your shaded area to be at .9 and you select above, you should see where 90% of the failures are expected to lie and this will be after 32.5596 months.
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