TickTock manufacturing is trying to determine the appropriat

Tick-Tock manufacturing is trying to determine the appropriate warranty period for its new line of \"Die Hard\" watches. After testing the watches, they have determined that the watches last, on average 4 years before they are in need of repair. The life expectancy of the watch is normally distributed and has a standard deviation of eight months. If Tick-Tock does not want to pay warranty claims on more than 5% of the watches, how many months should they set as the expiration of the warranty period?

Solution

P ( Z > x ) = 0.05
Value of z to the cumulative probability of 0.05 from normal table is 1.64
P( x-u/ (s.d) > x - 48/8) = 0.05
That is, ( x - 48/8) = 1.64
--> x = 1.64 * 8+48 = 61.16                  
warranty should be close 62 if the don\'t want to put not ore than 5%