A manufacturer plans to provide a warranty on a CD player. Assume that the set of failure times for the player is normally distributed with a mean time of 12,000 hours and a standard deviation of 2,000 hours. Assume that the typical purchaser will use the CD player for 5 hours per day. The manufacturer does not want more than 3% of the CD players returned as defective within the warranty period. What is the longest warranty period (in months) that will satisfy that criterion? (Assume that there are 31 days in each month.

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