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Research of a manufacturer of cell phones, shows that the average cell phone will be 26 months before there is a need of repairs. If the standard deviation for the data is 6 months, what length of time should the manufacturer set for a warranty such that less than 10% of all cell phones will need repairs during the warranty period?

Answer :

N = number of phones needing repair after a certain number of months
 
w = the number of months such that the integral under the normal distribution

curve centered at 26 with a standard deviation of 6 months = 0.10.

 Using that, I find that the warranty period should be 18.3 months.

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