The life expectancy of a item is normally distributed with a

The life expectancy of a item is normally distributed with a mean of 48 months with a standard deviation of 9 months. There is a 3 year warranty, how many will be in operating condition after the warranty expires

Solution

Note that 3 years = 36 months.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value = 36      
u = mean =    48      
          
s = standard deviation =    9      
          
Thus,          
          
z = (x - u) / s =    -1.333333333      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1.333333333   ) =    0.90878878 or 90.88% of items [ANSWER]