SOLUTION: The mean lifetime of a printer is 48 months, with a standard deviation of 7 months. If the distribution of the printer lifetime is normal, for how many months should a guarantee be

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Question 1174438: The mean lifetime of a printer is 48 months, with a standard deviation of 7 months. If the distribution of the printer lifetime is normal, for how many months should a guarantee be made if the manufacturer does not want to exchange more than 10% of the watches? Assume the variable is normally distributed. (Round up whatever you get for the number of months the guarantee should be given for.)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
  Normal Distribution:  μ = 48m  and   σ = 7mos 
manufacturer does not want to exchange more than 10% of the watches
z+=blue+%28x+-+mu%29%2Fblue%28sigma%29
  z = 1.282 represents 10% of the Standard Normal Curve
  
 1.282+=+blue+%28x+-+48%29%2Fblue%287%29
    x = 7(1.282) + 48 = 56.97 (rounding down to 56)  
90% are expected to have lifetime of 56mo
 For how many months should a guarantee be made:  56mo
Wish You the Best in your Studies.