LIFETIME OF DISHWASHER FOLLOWS NORMAL DISTRIBUTION WITH MEAN

LIFETIME OF DISHWASHER FOLLOWS NORMAL DISTRIBUTION WITH MEAN =8 YEARS AND STANDARD DEVIATION = 1.2 YEARS. THE COMPANY WILL REPLACE ANY DISHWASHER THAT FAILS DURING THE GUARANTEE PERIOD. HOW LONG SHOULD COMPANY\'S DISHWASHER BE GUARANTEED IF COMPANY WISHED TO REPLACE NO MORE THAN 2% OF DISHWASHERS?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.02      
          
Then, using table or technology,          
          
z =    -2.053748911      
          
As x = u + z * s,          
          
where          
          
u = mean =    8      
z = the critical z score =    -2.053748911      
s = standard deviation =    1.2      
          
Then          
          
x = critical value =    5.535501307 years [ANSWER]