Question 164665
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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