The length of life of a type of automatic washer is known to

The length of life of a type of automatic washer is known to be normally distributed with a mean of 8.3 years and a standard deviation of 1.2 years. For how many years should the manufacturer guarantee these automatic washers, if he wants to replace only 6% of the washers under the guarantee?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.06      
          
Then, using table or technology,          
          
z =    -1.554773595      
          
As x = u + z * s,          
          
where          
          
u = mean =    8.3      
z = the critical z score =    -1.554773595      
s = standard deviation =    1.2      
          
Then          
          
x = critical value =    6.434271686 YEARS [ANSWER]