Jessica president of City products is reviewing the warranty

Jessica, president of City products, is reviewing the warranty policy for her company\'s new model of automobile batteries. Life tests performed on a large number of batteries indicate: (1) an average of 75 months, (2) a standard deviation of 5 months & (3) battery life is approximately normally distributed. Approximately what percentage of the batteries will fail within the first 60 month of use?

A) 2.5% B) 0.15% C) 1% D) 5%

Solution

Normal Distribution
Mean ( u ) =75
Standard Deviation ( sd )=5
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 60) = (60-75)/5
= -15/5= -3
= P ( Z <-3) From Standard Normal Table
= 0.0013 = 0.13% ~ 1%